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// Upgraded to Delphi 2009: Sebastian Zierer
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(* ***** BEGIN LICENSE BLOCK *****
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* Version: MPL 1.1
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*
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* The contents of this file are subject to the Mozilla Public License Version
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* 1.1 (the "License"); you may not use this file except in compliance with
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* the License. You may obtain a copy of the License at
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* http://www.mozilla.org/MPL/
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*
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* Software distributed under the License is distributed on an "AS IS" basis,
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* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License
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* for the specific language governing rights and limitations under the
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* License.
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*
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* The Original Code is TurboPower SysTools
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*
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* The Initial Developer of the Original Code is
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* TurboPower Software
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*
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* Portions created by the Initial Developer are Copyright (C) 1996-2002
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* the Initial Developer. All Rights Reserved.
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*
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* Contributor(s):
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*
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* ***** END LICENSE BLOCK ***** *)
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{*********************************************************}
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{* SysTools: StStat.pas 4.04 *}
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{*********************************************************}
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{* SysTools: Statistical math functions modeled on *}
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{* those in Excel *}
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{*********************************************************}
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{$I StDefine.inc}
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unit StStat;
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{ The statistical distribution functions return results in singles }
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{ since the fractional accuracy of these is typically about 3e-7. }
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interface
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uses
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Windows,
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{$IFDEF UseMathUnit}
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Math,
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{$ELSE}
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StMath,
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{$ENDIF}
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SysUtils, StConst, StBase;
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{AVEDEV}
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function AveDev(const Data: array of Double) : Double;
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function AveDev16(const Data; NData : Integer) : Double;
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{-Returns the average of the absolute deviations of data points from their
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mean. AveDev is a measure of the variability in a data set.
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}
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{CONFIDENCE}
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function Confidence(Alpha, StandardDev : Double; Size : LongInt) : Double;
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{-Returns the confidence interval for a population mean.
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The confidence interval is a range on either side of a sample mean.
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Alpha is the significance level used to compute the confidence level.
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The confidence level equals 100*(1 - Alpha)%, or in other words,
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an Alpha of 0.05 indicates a 95 percent confidence level.
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StandardDev is the population standard deviation for the data range
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and is assumed to be known.
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Size is the sample Size.
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}
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{CORREL}
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function Correlation(const Data1, Data2 : array of Double) : Double;
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function Correlation16(const Data1, Data2; NData : Integer) : Double;
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{-Returns the correlation coefficient of the Data1 and Data2 arrays.
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Use the correlation coefficient to determine the relationship between
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two data sets.
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This function also returns the same value as the PEARSON function
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in Excel.
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}
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{COVAR}
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function Covariance(const Data1, Data2 : array of Double) : Double;
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function Covariance16(const Data1, Data2; NData : Integer) : Double;
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{-Returns covariance, the average of products of deviations, for the Data1
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and Data2 arrays. Use covariance to determine the relationship between
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two data sets.
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}
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{DEVSQ}
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function DevSq(const Data : array of Double) : Double;
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function DevSq16(const Data; NData : Integer) : Double;
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{-Returns the sum of squares of deviations of data points from their
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sample mean.
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}
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{FREQUENCY}
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procedure Frequency(const Data : array of Double; const Bins : array of Double;
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var Counts : array of LongInt);
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procedure Frequency16(const Data; NData : Integer; const Bins; NBins : Integer;
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var Counts);
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{-Calculates how often values occur within an array of data,
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and then returns an array of counts.
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Data is an array of values for which you want to count frequencies.
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Bins is an array of intervals into which you want to group the values in
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Data.
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Counts is an array into which the frequency counts are returned. Counts
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must have one more element than does Bins. The first element of Counts
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has all items less than the first number in Bins. The next element of
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Counts is the items that fall between Bins[0] and Bins[1]. The last
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element of Counts has all items greater than the last number in Bins.
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}
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{GEOMEAN}
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function GeometricMean(const Data : array of Double) : Double;
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function GeometricMean16(const Data; NData : Integer) : Double;
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{-Returns the geometric mean of an array of positive data. The geometric
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mean is the n'th root of the product of n positive numbers.}
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{HARMEAN}
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function HarmonicMean(const Data : array of Double) : Double;
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function HarmonicMean16(const Data; NData : Integer) : Double;
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{-Returns the harmonic mean of an array of data. The harmonic mean is the
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reciprocal of the arithmetic mean of reciprocals.}
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{LARGE}
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function Largest(const Data : array of Double; K : Integer) : Double;
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function Largest16(const Data; NData : Integer; K : Integer) : Double;
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{-Returns the K'th largest value in an array of data. You can use this
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function to select a value based on its relative standing.}
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{MEDIAN}
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function Median(const Data : array of Double) : Double;
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function Median16(const Data; NData : Integer) : Double;
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{-Returns the median of the given numbers. The median is the number in the
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middle of a set of numbers; that is, half the numbers have values that
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are greater than the median, and half have values that are less.
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If there is an even number of numbers in the set, MEDIAN calculates
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the average of the two numbers in the middle.
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}
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{MODE}
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function Mode(const Data: array of Double) : Double;
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function Mode16(const Data; NData : Integer) : Double;
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{-Returns the most frequently occurring, or repetitive, value in an array
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of data. In case of duplicate frequencies it returns the smallest
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such value.}
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{PERCENTILE}
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function Percentile(const Data : array of Double; K : Double) : Double;
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function Percentile16(const Data; NData : Integer; K : Double) : Double;
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{-Returns the value of the K'th percentile of an array of data.
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K is the percentile value, a number between 0 and 1. If K is not a
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multiple of 1/(n-1) where n is the size of Data, Percentile
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interpolates between the closest bins.
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}
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{PERCENTRANK}
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function PercentRank(const Data : array of Double; X : Double) : Double;
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function PercentRank16(const Data; NData : Integer; X : Double) : Double;
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{-Returns the percentile position of a value within an array of data.
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X is a data value. If X is not found within the array, PercentRank
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interpolates between the closest data points.
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}
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{PERMUT}
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function Permutations(Number, NumberChosen : Integer) : Extended;
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{-Returns the number of permutations for a given Number of objects that
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can be selected from Number objects. A permutation is any set or subset
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of objects or events where internal order is significant.
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Permutations are different from combinations, for which the internal order
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is not significant.
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Number is an Integer that describes the number of objects.
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NumberChosen is an Integer that describes the number of objects in
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each permutation.
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}
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{COMBIN}
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function Combinations(Number, NumberChosen : Integer) : Extended;
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{-Returns the number of combinations for a given Number of objects that
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can be selected from Number objects. A combination is any set or subset
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of objects or events where internal order is not significant.
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Number is an Integer that describes the number of objects.
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NumberChosen is an Integer that describes the number of objects in
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each permutation.
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}
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{FACT}
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function Factorial(N : Integer) : Extended;
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{-Returns N! as a floating point number.
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Extended is used for range, not accuracy.
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}
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{RANK}
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function Rank(Number : Double; const Data : array of Double;
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Ascending : Boolean) : Integer;
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function Rank16(Number : Double; const Data; NData : Integer;
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Ascending : Boolean) : Integer;
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{-Returns the rank of a number in a list of numbers. If you were to sort
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a list that contained no duplicates, the rank of the Number would be its
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position within the sorted list.
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Number is the number whose rank you want.
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Data is the list of numbers.
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If Ascending is True the rank is measured from the beginning of the
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array; otherwise from the end of the array.
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If the Number is not found in the array, 0 is returned. Numbers that
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appear multiple times all have the same rank, but they affect the
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rank of numbers appearing after them. For example, in a list of
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Integers, if the number 10 appears twice and has a rank of 5,
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then 11 would have a rank of 7 (no number would have a rank of 6).
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Be sure to sort Data before calling this routine if you want an
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unambiguous ranking.
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}
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{SMALL}
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function Smallest(const Data : array of Double; K : Integer) : Double;
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function Smallest16(const Data; NData : Integer; K : Integer) : Double;
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{-Returns the K'th smallest value in an array of data. You can use this
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function to select a value based on its relative standing.}
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{TRIMMEAN}
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function TrimMean(const Data : array of Double; Percent : Double) : Double;
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function TrimMean16(const Data; NData : Integer; Percent : Double) : Double;
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{-Returns the mean of Data after trimming Percent points from the data set.
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If Percent is 0.2 and there are 20 points in Data, the 2 largest and 2
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smallest points would be dropped before computing the mean. Percent must
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be a number between 0 and 1.
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}
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{--------------------------------------------------------------------------}
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type
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{full statistics for a linear regression}
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TStLinEst = record
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B0, B1 : Double; {model coefficients}
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seB0, seB1 : Double; {standard error of model coefficients}
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R2 : Double; {coefficient of determination}
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sigma : Double; {standard error of regression}
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SSr, SSe : Double; {elements for ANOVA table}
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F0 : Double; {F-statistic to test B1=0}
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df : Integer; {denominator degrees of freedom for F-statistic}
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end;
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{LINEST}
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procedure LinEst(const KnownY : array of Double;
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const KnownX : array of Double; var LF : TStLinEst; ErrorStats : Boolean);
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procedure LinEst16(const KnownY; const KnownX; NData : Integer;
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var LF : TStLinEst; ErrorStats : Boolean);
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{-Performs linear fit to data and returns coefficients and error
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statistics.
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KnownY is the dependent array of known data points.
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KnownX is the independent array of known data points.
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NData must be greater than 2.
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If ErrorStats is FALSE, only B0 and B1 are computed; the other fields
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of TStLinEst are set to 0.0.
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See declaration of TStLinEst for returned data.
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}
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{LOGEST}
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procedure LogEst(const KnownY : array of Double;
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const KnownX : array of Double; var LF : TStLinEst; ErrorStats : Boolean);
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procedure LogEst16(const KnownY; const KnownX; NData : Integer;
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var LF : TStLinEst; ErrorStats : Boolean);
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{-Performs log-linear fit to data and returns coefficients and error
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statistics.
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KnownY is the dependent array of known data points.
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KnownX is the independent array of known data points.
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NData must be greater than 2.
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KnownY is transformed using ln(KnownY) before fitting:
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y = B0*B1^x implies that ln(y) = ln(B0)+X*ln(B1)
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In the returned LF, B0 and B1 are returned as shown. Other values in LF
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are in terms of the log transformation.
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If ErrorStats is FALSE, only B0 and B1 are computed; the other fields
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of TStLinEst are set to 0.0.
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See declaration of TStLinEst for returned data.
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}
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{FORECAST}
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function Forecast(X : Double; const KnownY: array of Double;
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const KnownX : array of Double) : Double;
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function Forecast16(X : Double; const KnownY; const KnownX;
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NData : Integer) : Double;
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{-Calculates a future value by using existing values. The predicted value
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is a y-value for a given X-value. The known values are existing X-values
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and y-values, and the new value is predicted by using linear regression.
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X is the data point for which you want to predict a value.
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KnownY is the dependent array of known data points.
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KnownX is the independent array of known data points.
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}
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{similar to GROWTH but more consistent with FORECAST}
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function ForecastExponential(X : Double; const KnownY : array of Double;
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const KnownX : array of Double) : Double;
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function ForecastExponential16(X : Double; const KnownY; const KnownX;
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NData : Integer) : Double;
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{-Calculates a future value by using existing values. The predicted value
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is a y-value for a given X-value. The known values are existing X-values
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and y-values, and the new value is predicted by using linear regression
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to an exponential growth model, y = B0*B1^X.
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X is the data point for which you want to predict a value.
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KnownY is the dependent array of known data points.
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KnownX is the independent array of known data points.
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}
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{INTERCEPT}
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function Intercept(const KnownY : array of Double;
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const KnownX : array of Double) : Double;
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function Intercept16(const KnownY; const KnownX; NData : Integer) : Double;
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{-Calculates the point at which a line will intersect the y-axis by using
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existing X-values and y-values. The intercept point is based on a best-fit
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regression line plotted through the known X-values and known y-values.
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Use the intercept when you want to determine the value of the dependent
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variable when the independent variable is 0 (zero).
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}
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{RSQ}
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function RSquared(const KnownY : array of Double;
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const KnownX : array of Double) : Double;
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function RSquared16(const KnownY; const KnownX; NData : Integer) : Double;
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{-Returns the square of the Pearson product moment correlation coefficient
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through data points in KnownY's and KnownX's. The r-squared value can
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be interpreted as the proportion of the variance in y attributable to
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the variance in X.
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}
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{SLOPE}
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function Slope(const KnownY : array of Double;
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const KnownX : array of Double) : Double;
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function Slope16(const KnownY; const KnownX; NData : Integer) : Double;
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{-Returns the slope of the linear regression line through data points in
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KnownY's and KnownX's. The slope is the vertical distance divided by the
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horizontal distance between any two points on the line, which is the rate
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of change along the regression line.
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}
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{STEYX}
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function StandardErrorY(const KnownY : array of Double;
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const KnownX : array of Double) : Double;
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function StandardErrorY16(const KnownY; const KnownX;
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NData : Integer) : Double;
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{-Returns the standard error of the predicted y-value for each X in a linear
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regression. The standard error is a measure of the amount of error in the
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prediction of y for an individual X.
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}
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{--------------------------------------------------------------------------}
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{BETADIST}
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function BetaDist(X, Alpha, Beta, A, B : Single) : Single;
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{-Returns the cumulative beta probability density function.
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The cumulative beta probability density function is commonly used to
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study variation in the percentage of something across samples.
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X is the value at which to evaluate the function, A <= X <= B.
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Alpha is a parameter to the distribution.
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Beta is a parameter to the distribution.
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A is the lower bound to the interval of X.
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B is the upper bound to the interval of X.
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The standard beta distribution has A=0 and B=1.
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Fractional error less than 3.0e-7.
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}
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{BETAINV}
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function BetaInv(Probability, Alpha, Beta, A, B : Single) : Single;
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{-Returns the inverse of the cumulative beta probability density function.
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That is, if Probability = BetaDist(X,...), then
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BetaInv(Probability,...) = X.
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Probability is a probability (0 <= p <= 1) associated with the
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beta distribution.
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Alpha is a parameter to the distribution.
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Beta is a parameter to the distribution.
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A is the lower bound to the interval of the distribution.
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B is the upper bound to the interval of the distribution.
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Fractional error less than 3.0e-7.
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}
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{BINOMDIST}
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function BinomDist(NumberS, Trials : Integer; ProbabilityS : Single;
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Cumulative : Boolean) : Single;
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{-Returns the individual term binomial distribution probability.
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Use BinomDist in problems with a fixed number of tests or Trials,
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when the outcomes of any trial are only success or failure,
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when Trials are independent, and when the probability of success is
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constant throughout the experiment.
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NumberS is the number of successes in Trials.
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Trials is the number of independent trials.
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ProbabilityS is the probability of success on each trial.
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Cumulative is a logical value that determines the form of the function.
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If Cumulative is TRUE, then BinomDist returns the cumulative
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distribution function, which is the probability that there are at most
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NumberS successes; if FALSE, it returns the probability mass function,
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which is the probability that there are NumberS successes.
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}
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{CRITBINOM}
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function CritBinom(Trials : Integer; ProbabilityS, Alpha : Single) : Integer;
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{-Returns the smallest value for which the cumulative binomial distribution
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is greater than or equal to a criterion value.
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Trials is the number of Bernoulli trials.
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ProbabilityS is the probability of a success on each trial.
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Alpha is the criterion value.
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}
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{CHIDIST}
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function ChiDist(X : Single; DegreesFreedom : Integer) : Single;
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{-Returns the one-tailed probability of the chi-squared distribution.
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The chi-squared distribution is associated with a chi-squared test.
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Use the chi-squared test to compare observed and expected values.
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X is the value at which you want to evaluate the distribution.
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DegreesFreedom is the number of degrees of freedom.
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}
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{CHIINV}
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function ChiInv(Probability : Single; DegreesFreedom : Integer) : Single;
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{-Returns the inverse of the one-tailed probability of the chi-squared
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distribution. If Probability = ChiDist(X,...), then
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ChiInv(Probability,...) = X.
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Probability is a probability associated with the chi-squared
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distribution.
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DegreesFreedom is the number of degrees of freedom.
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}
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{EXPONDIST}
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function ExponDist(X, Lambda : Single; Cumulative : Boolean) : Single;
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{-Returns the exponential distribution. Use ExponDist to model the time
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between events.
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X is the value of the function.
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Lambda is the parameter value.
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Cumulative is a logical value that indicates which form of the
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exponential function to provide. If Cumulative is TRUE, ExponDist
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returns the cumulative distribution function; if FALSE, it returns
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the probability density function.
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}
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{FDIST}
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function FDist(X : Single; DegreesFreedom1, DegreesFreedom2 : Integer) : Single;
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{-Returns the F probability distribution. You can use this function to
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determine whether two data sets have different degrees of diversity.
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X is the value at which to evaluate the function.
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DegreesFreedom1 is the numerator degrees of freedom.
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DegreesFreedom2 is the denominator degrees of freedom.
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Fractional error less than 3.0e-7.
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}
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{FINV}
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function FInv(Probability : Single;
|
447 |
DegreesFreedom1, DegreesFreedom2 : Integer) : Single;
|
448 |
{-Returns the inverse of the F probability distribution. If
|
449 |
p = FDist(X,...), then FInv(p,...) = X.
|
450 |
Probability is a probability associated with the F cumulative
|
451 |
distribution.
|
452 |
DegreesFreedom1 is the numerator degrees of freedom.
|
453 |
DegreesFreedom2 is the denominator degrees of freedom.
|
454 |
Fractional error less than 3.0e-7.
|
455 |
}
|
456 |
|
457 |
{LOGNORMDIST}
|
458 |
function LogNormDist(X, Mean, StandardDev : Single) : Single;
|
459 |
{-Returns the cumulative lognormal distribution of X, where ln(X) is
|
460 |
normally distributed with parameters Mean and StandardDev.
|
461 |
Use this function to analyze data that has been logarithmically
|
462 |
transformed.
|
463 |
X is the value at which to evaluate the function.
|
464 |
Mean is the mean of ln(X).
|
465 |
StandardDev is the standard deviation of ln(X).
|
466 |
}
|
467 |
|
468 |
{LOGINV}
|
469 |
function LogInv(Probability, Mean, StandardDev : Single) : Single;
|
470 |
{-Returns the inverse of the lognormal cumulative distribution function of
|
471 |
X, where ln(X) is normally distributed with parameters Mean and
|
472 |
StandardDev. If p = LogNormDist(X,...) then LogInv(p,...) = X.
|
473 |
Probability is a probability associated with the lognormal distribution.
|
474 |
Mean is the mean of ln(X).
|
475 |
StandardDev is the standard deviation of ln(X).
|
476 |
}
|
477 |
|
478 |
{NORMDIST}
|
479 |
function NormDist(X, Mean, StandardDev : Single; Cumulative : Boolean) : Single;
|
480 |
{-Returns the normal cumulative distribution for the specified Mean and
|
481 |
standard deviation.
|
482 |
X is the value for which you want the distribution.
|
483 |
Mean is the arithmetic mean of the distribution.
|
484 |
StandardDev is the standard deviation of the distribution.
|
485 |
Cumulative is a logical value that determines the form of the function.
|
486 |
If Cumulative is TRUE, NormDist returns the cumulative distribution
|
487 |
function; if FALSE, it returns the probability density function.
|
488 |
}
|
489 |
|
490 |
{NORMINV}
|
491 |
function NormInv(Probability, Mean, StandardDev : Single) : Single;
|
492 |
{-Returns the inverse of the normal cumulative distribution for the
|
493 |
specified mean and standard deviation.
|
494 |
Probability is a probability corresponding to the normal distribution.
|
495 |
Mean is the arithmetic mean of the distribution.
|
496 |
StandardDev is the standard deviation of the distribution.
|
497 |
}
|
498 |
|
499 |
{NORMSDIST}
|
500 |
function NormSDist(Z : Single) : Single;
|
501 |
{-Returns the standard normal cumulative distribution function.
|
502 |
The distribution has a mean of 0 (zero) and a standard deviation of one.
|
503 |
Z is the value for which you want the distribution.
|
504 |
}
|
505 |
|
506 |
{NORMSINV}
|
507 |
function NormSInv(Probability : Single) : Single;
|
508 |
{-Returns the inverse of the standard normal cumulative distribution.
|
509 |
The distribution has a mean of zero and a standard deviation of one.
|
510 |
Probability is a probability corresponding to the normal distribution.
|
511 |
}
|
512 |
|
513 |
{POISSON}
|
514 |
function Poisson(X : Integer; Mean : Single; Cumulative : Boolean) : Single;
|
515 |
{-Returns the Poisson distribution.
|
516 |
X is the number of events.
|
517 |
Mean is the expected numeric value.
|
518 |
Cumulative is a logical value that determines the form of the
|
519 |
probability distribution returned. If Cumulative is TRUE, Poisson
|
520 |
returns the cumulative Poisson probability that the number of random
|
521 |
events occurring will be between zero and X inclusive; if FALSE,
|
522 |
it returns the Poisson probability mass function that the number of
|
523 |
events occurring will be exactly X.
|
524 |
}
|
525 |
|
526 |
{TDIST}
|
527 |
function TDist(X : Single; DegreesFreedom : Integer; TwoTails : Boolean) : Single;
|
528 |
{-Returns the Student's t-distribution. The t-distribution is used in the
|
529 |
hypothesis testing of small sample data sets. Use this function in place
|
530 |
of a table of critical values for the t-distribution.
|
531 |
X is the numeric value at which to evaluate the distribution.
|
532 |
DegreesFreedom is an Integer indicating the number of degrees of freedom.
|
533 |
TwoTails if a logical value that indicates the number of distribution
|
534 |
tails to return. If FALSE, TDist returns the one-tailed distribution;
|
535 |
otherwise it returns the two-tailed distribution.
|
536 |
}
|
537 |
|
538 |
{TINV}
|
539 |
function TInv(Probability : Single; DegreesFreedom : Integer) : Single;
|
540 |
{-Returns the inverse of the Student's t-distribution for the specified
|
541 |
degrees of freedom.
|
542 |
Probability is the probability associated with the two-tailed Student's
|
543 |
t-distribution.
|
544 |
DegreesFreedom is the number of degrees of freedom to characterize
|
545 |
the distribution.
|
546 |
}
|
547 |
|
548 |
{--------------------------------------------------------------------------}
|
549 |
{undocumented functions you can call if you need}
|
550 |
|
551 |
function Erfc(X : Single) : Single;
|
552 |
{-Returns the complementary error function with fractional error
|
553 |
everywhere less than 1.2e-7. X is any finite value.
|
554 |
}
|
555 |
|
556 |
function GammaLn(X : Single) : Single;
|
557 |
{-Returns ln(Gamma(X)) where X > 0.0.}
|
558 |
|
559 |
{--------------------------------------------------------------------------}
|
560 |
|
561 |
{.$DEFINE Debug}
|
562 |
{$IFDEF Debug}
|
563 |
{like Largest and Smallest but using slower simpler algorithm}
|
564 |
function LargestSort(const Data: array of Double; K : Integer) : Double;
|
565 |
function SmallestSort(const Data: array of double; K : Integer) : Double;
|
566 |
{$ENDIF}
|
567 |
|
568 |
implementation
|
569 |
|
570 |
procedure RaiseStatError(Code : LongInt);
|
571 |
{-Generate a statistics exception}
|
572 |
var
|
573 |
E : EStStatError;
|
574 |
begin
|
575 |
E := EStStatError.CreateResTP(Code, 0);
|
576 |
E.ErrorCode := Code;
|
577 |
raise E;
|
578 |
end;
|
579 |
|
580 |
procedure DoubleArraySort(var Data; NData : Integer);
|
581 |
{-Heapsort an array of Doubles into Ascending order}
|
582 |
type
|
583 |
TDoubleArray1 = array[1..StMaxBlockSize div SizeOf(Double)] of Double;
|
584 |
var
|
585 |
i : Integer;
|
586 |
T : Double;
|
587 |
DA : TDoubleArray1 absolute Data;
|
588 |
|
589 |
procedure Adjust(i, N : Integer);
|
590 |
var
|
591 |
j : Integer;
|
592 |
S : Double;
|
593 |
begin
|
594 |
{j is left child of i}
|
595 |
j := 2*i;
|
596 |
{save i'th element temporarily}
|
597 |
S := DA[i];
|
598 |
while (j <= N) do begin
|
599 |
{compare left and right child}
|
600 |
if (j < N) and (DA[j] < DA[j+1]) then
|
601 |
{j indexes larger child}
|
602 |
inc(j);
|
603 |
if (S >= DA[j]) then
|
604 |
{a position for item is found}
|
605 |
break;
|
606 |
{move the larger child up a level}
|
607 |
DA[j shr 1] := DA[j];
|
608 |
{look at left child of j}
|
609 |
j := j shl 1;
|
610 |
end;
|
611 |
{store saved item}
|
612 |
DA[j shr 1] := S;
|
613 |
end;
|
614 |
|
615 |
begin
|
616 |
{transform the elements into a heap}
|
617 |
for i := (NData shr 1) downto 1 do
|
618 |
Adjust(i, NData);
|
619 |
|
620 |
{repeatedly exchange the maximum at top of heap with the last element}
|
621 |
for i := NData downto 2 do begin
|
622 |
T := DA[1];
|
623 |
DA[1] := DA[i];
|
624 |
DA[i] := T;
|
625 |
{update the heap for the remaining elements}
|
626 |
Adjust(1, i-1);
|
627 |
end;
|
628 |
end;
|
629 |
|
630 |
function CopyAndSort(const Data; NData : Integer;
|
631 |
var SD : PDoubleArray) : Cardinal;
|
632 |
{-Allocates heap space for an array copy, moves data, sorts, and returns size}
|
633 |
var
|
634 |
Size : LongInt;
|
635 |
begin
|
636 |
Size := LongInt(NData)*sizeof(Double);
|
637 |
{if (Size > MaxBlockSize) then}
|
638 |
{ RaiseStatError(stscStatBadCount);}
|
639 |
Result := Size;
|
640 |
getmem(SD, Size); {raises exception if insufficient memory}
|
641 |
try
|
642 |
move(Data, SD^, Size);
|
643 |
DoubleArraySort(SD^, NData);
|
644 |
except
|
645 |
freemem(SD, Size);
|
646 |
raise;
|
647 |
end;
|
648 |
end;
|
649 |
|
650 |
function AveDev(const Data: array of Double) : Double;
|
651 |
begin
|
652 |
Result := AveDev16(Data, High(Data)+1);
|
653 |
end;
|
654 |
|
655 |
function Mean(const Data; NData : Integer) : Extended;
|
656 |
{-Computes the mean of an array of Doubles}
|
657 |
var
|
658 |
i : Integer;
|
659 |
s : Extended;
|
660 |
begin
|
661 |
s := 0.0;
|
662 |
for I := 0 to NData-1 do
|
663 |
s := s+TDoubleArray(Data)[I];
|
664 |
Result := s/NData;
|
665 |
end;
|
666 |
|
667 |
function AveDev16(const Data; NData : Integer) : Double;
|
668 |
var
|
669 |
i : Integer;
|
670 |
m, s : Extended;
|
671 |
begin
|
672 |
if (NData <= 0) then
|
673 |
RaiseStatError(stscStatBadCount);
|
674 |
|
675 |
{compute sum of absolute deviations}
|
676 |
m := Mean(Data, NData);
|
677 |
s := 0.0;
|
678 |
for i := 0 to NData-1 do
|
679 |
s := s+abs(TDoubleArray(Data)[i]-m);
|
680 |
|
681 |
Result := s/NData;
|
682 |
end;
|
683 |
|
684 |
function Confidence(Alpha, StandardDev : Double; Size : LongInt) : Double;
|
685 |
begin
|
686 |
if (StandardDev <= 0) or (Size < 1) then
|
687 |
RaiseStatError(stscStatBadParam);
|
688 |
Result := NormSInv(1.0-Alpha/2.0)*StandardDev/sqrt(Size);
|
689 |
end;
|
690 |
|
691 |
function Correlation(const Data1, Data2 : array of Double) : Double;
|
692 |
begin
|
693 |
if (High(Data1) <> High(Data2)) then
|
694 |
RaiseStatError(stscStatBadCount);
|
695 |
Result := Correlation16(Data1, Data2, High(Data1)+1);
|
696 |
end;
|
697 |
|
698 |
function Correlation16(const Data1, Data2; NData : Integer) : Double;
|
699 |
var
|
700 |
sx, sy, xmean, ymean, sxx, sxy, syy, x, y : Extended;
|
701 |
i : Integer;
|
702 |
begin
|
703 |
if (NData <= 1) then
|
704 |
RaiseStatError(stscStatBadCount);
|
705 |
|
706 |
{compute basic sums}
|
707 |
sx := 0.0;
|
708 |
sy := 0.0;
|
709 |
sxx := 0.0;
|
710 |
sxy := 0.0;
|
711 |
syy := 0.0;
|
712 |
for i := 0 to NData-1 do begin
|
713 |
x := TDoubleArray(Data1)[i];
|
714 |
y := TDoubleArray(Data2)[i];
|
715 |
sx := sx+x;
|
716 |
sy := sy+y;
|
717 |
sxx := sxx+x*x;
|
718 |
syy := syy+y*y;
|
719 |
sxy := sxy+x*y;
|
720 |
end;
|
721 |
xmean := sx/NData;
|
722 |
ymean := sy/NData;
|
723 |
sxx := sxx-NData*xmean*xmean;
|
724 |
syy := syy-NData*ymean*ymean;
|
725 |
sxy := sxy-NData*xmean*ymean;
|
726 |
|
727 |
Result := sxy/sqrt(sxx*syy);
|
728 |
end;
|
729 |
|
730 |
function Covariance(const Data1, Data2 : array of Double) : Double;
|
731 |
begin
|
732 |
if (High(Data1) <> High(Data2)) then
|
733 |
RaiseStatError(stscStatBadCount);
|
734 |
Result := Covariance16(Data1, Data2, High(Data1)+1);
|
735 |
end;
|
736 |
|
737 |
function Covariance16(const Data1, Data2; NData : Integer) : Double;
|
738 |
var
|
739 |
sx, sy, xmean, ymean, sxy, x, y : Extended;
|
740 |
i : Integer;
|
741 |
begin
|
742 |
if (NData <= 1) then
|
743 |
RaiseStatError(stscStatBadCount);
|
744 |
|
745 |
{compute basic sums}
|
746 |
sx := 0.0;
|
747 |
sy := 0.0;
|
748 |
sxy := 0.0;
|
749 |
for i := 0 to NData-1 do begin
|
750 |
x := TDoubleArray(Data1)[i];
|
751 |
y := TDoubleArray(Data2)[i];
|
752 |
sx := sx+x;
|
753 |
sy := sy+y;
|
754 |
sxy := sxy+x*y;
|
755 |
end;
|
756 |
xmean := sx/NData;
|
757 |
ymean := sy/NData;
|
758 |
sxy := sxy-NData*xmean*ymean;
|
759 |
|
760 |
Result := sxy/NData;
|
761 |
end;
|
762 |
|
763 |
function DevSq(const Data: array of Double) : Double;
|
764 |
begin
|
765 |
Result := DevSq16(Data, High(Data)+1);
|
766 |
end;
|
767 |
|
768 |
function DevSq16(const Data; NData : Integer) : Double;
|
769 |
var
|
770 |
i : Integer;
|
771 |
sx, sxx, x : Extended;
|
772 |
begin
|
773 |
if (NData <= 0) then
|
774 |
RaiseStatError(stscStatBadCount);
|
775 |
|
776 |
sx := 0.0;
|
777 |
sxx := 0.0;
|
778 |
for i := 0 to NData-1 do begin
|
779 |
x := TDoubleArray(Data)[i];
|
780 |
sx := sx+x;
|
781 |
sxx := sxx+x*x;
|
782 |
end;
|
783 |
Result := sxx-sqr(sx)/NData;
|
784 |
end;
|
785 |
|
786 |
procedure Frequency(const Data: array of Double; const Bins: array of Double;
|
787 |
var Counts: array of LongInt);
|
788 |
begin
|
789 |
if (High(Counts) <= High(Bins)) then
|
790 |
RaiseStatError(stscStatBadCount);
|
791 |
Frequency16(Data, High(Data)+1, Bins, High(Bins)+1, Counts);
|
792 |
end;
|
793 |
|
794 |
procedure Frequency16(const Data; NData : Integer; const Bins; NBins : Integer;
|
795 |
var Counts);
|
796 |
var
|
797 |
b, i : Integer;
|
798 |
Size : Cardinal;
|
799 |
SD : PDoubleArray;
|
800 |
begin
|
801 |
if (NData <= 0) or (NBins <= 0) then
|
802 |
RaiseStatError(stscStatBadCount);
|
803 |
|
804 |
{copy and sort array}
|
805 |
Size := CopyAndSort(Data, NData, SD);
|
806 |
try
|
807 |
{initialize all counts to zero}
|
808 |
fillchar(Counts, (NBins+1)*sizeof(Integer), 0);
|
809 |
|
810 |
{scan all data elements, putting into correct bin}
|
811 |
b := 0;
|
812 |
i := 0;
|
813 |
while (i < NData) do begin
|
814 |
if (SD^[i] <= TDoubleArray(Bins)[b]) then begin
|
815 |
{current data element falls into this bin}
|
816 |
inc(TIntArray(Counts)[b]);
|
817 |
inc(i);
|
818 |
end else begin
|
819 |
{move to next bin that collects data}
|
820 |
repeat
|
821 |
inc(b);
|
822 |
until (b = NBins) or (TDoubleArray(Bins)[b] > SD^[i]);
|
823 |
if (b = NBins) then begin
|
824 |
{add remaining elements to the catchall bin}
|
825 |
inc(TIntArray(Counts)[b], NData-i);
|
826 |
i := NData;
|
827 |
end;
|
828 |
end;
|
829 |
end;
|
830 |
|
831 |
finally
|
832 |
freemem(SD, Size);
|
833 |
end;
|
834 |
end;
|
835 |
|
836 |
function GeometricMean(const Data: array of Double) : Double;
|
837 |
begin
|
838 |
Result := GeometricMean16(Data, High(Data)+1);
|
839 |
end;
|
840 |
|
841 |
function GeometricMean16(const Data; NData : Integer) : Double;
|
842 |
var
|
843 |
i : Integer;
|
844 |
s, t : Extended;
|
845 |
begin
|
846 |
if (NData <= 0) then
|
847 |
RaiseStatError(stscStatBadCount);
|
848 |
|
849 |
s := 1.0;
|
850 |
for i := 0 to NData-1 do begin
|
851 |
t := TDoubleArray(Data)[i];
|
852 |
if (t <= 0.0) then
|
853 |
RaiseStatError(stscStatBadData);
|
854 |
s := s*t;
|
855 |
end;
|
856 |
|
857 |
Result := Power(s, 1.0/NData);
|
858 |
end;
|
859 |
|
860 |
function HarmonicMean(const Data: array of Double) : Double;
|
861 |
begin
|
862 |
Result := HarmonicMean16(Data, High(Data)+1);
|
863 |
end;
|
864 |
|
865 |
function HarmonicMean16(const Data; NData : Integer) : Double;
|
866 |
var
|
867 |
i : Integer;
|
868 |
s, t : Extended;
|
869 |
begin
|
870 |
if (NData <= 0) then
|
871 |
RaiseStatError(stscStatBadCount);
|
872 |
|
873 |
s := 0.0;
|
874 |
for i := 0 to NData-1 do begin
|
875 |
t := TDoubleArray(Data)[i];
|
876 |
if (t = 0.0) then
|
877 |
RaiseStatError(stscStatBadData);
|
878 |
s := s+(1.0/t);
|
879 |
end;
|
880 |
Result := NData/s;
|
881 |
end;
|
882 |
|
883 |
function Largest(const Data: array of Double; K : Integer) : Double;
|
884 |
begin
|
885 |
Result := Largest16(Data, High(Data)+1, K);
|
886 |
end;
|
887 |
|
888 |
function Largest16(const Data; NData : Integer; K : Integer) : Double;
|
889 |
var
|
890 |
b, t, i, j : integer;
|
891 |
Size : LongInt;
|
892 |
temp, pval : Double;
|
893 |
SD : PDoubleArray;
|
894 |
begin
|
895 |
if (NData <= 0) then
|
896 |
RaiseStatError(stscStatBadCount);
|
897 |
if (K <= 0) or (K > NData) then
|
898 |
RaiseStatError(stscStatBadParam);
|
899 |
|
900 |
Size := LongInt(NData)*sizeof(Double);
|
901 |
{if (Size > MaxBlockSize) then}
|
902 |
{ RaiseStatError(stscStatBadCount);}
|
903 |
getmem(SD, Size); {raises exception if insufficient memory}
|
904 |
try
|
905 |
move(Data, SD^, Size);
|
906 |
|
907 |
{make K 0-based}
|
908 |
dec(K);
|
909 |
|
910 |
{use quicksort-like selection}
|
911 |
b := 0;
|
912 |
t := NData-1;
|
913 |
while (t > b) do begin
|
914 |
{use random pivot in case of already-sorted data}
|
915 |
pval := SD^[b+random(t-b+1)];
|
916 |
i := b;
|
917 |
j := t;
|
918 |
repeat
|
919 |
while (SD^[i] > pval) do
|
920 |
inc(i);
|
921 |
while (pval > SD^[j]) do
|
922 |
dec(j);
|
923 |
if (i <= j) then begin
|
924 |
temp := SD^[i];
|
925 |
SD^[i] := SD^[j];
|
926 |
SD^[j] := temp;
|
927 |
inc(i);
|
928 |
dec(j);
|
929 |
end;
|
930 |
until (i > j);
|
931 |
if (j < K) then
|
932 |
b := i;
|
933 |
if (K < i) then
|
934 |
t := j;
|
935 |
end;
|
936 |
Result := SD^[K];
|
937 |
|
938 |
finally
|
939 |
freemem(SD, Size);
|
940 |
end;
|
941 |
end;
|
942 |
|
943 |
{debug version of Largest: slower but simpler}
|
944 |
{$IFDEF Debug}
|
945 |
function LargestSort(const Data: array of Double; K : Integer) : Double;
|
946 |
var
|
947 |
Size : Cardinal;
|
948 |
NData : Integer;
|
949 |
SD : PDoubleArray;
|
950 |
begin
|
951 |
NData := High(Data)+1;
|
952 |
if (NData <= 0) then
|
953 |
RaiseStatError(stscStatBadCount);
|
954 |
if (K <= 0) or (K > NData) then
|
955 |
RaiseStatError(stscStatBadParam);
|
956 |
|
957 |
{copy and sort array}
|
958 |
Size := CopyAndSort(Data, NData, SD);
|
959 |
try
|
960 |
{K=1 returns largest value, K=NData returns smallest}
|
961 |
Result := SD^[NData-K];
|
962 |
finally
|
963 |
freemem(SD, Size);
|
964 |
end;
|
965 |
end;
|
966 |
{$ENDIF}
|
967 |
|
968 |
function Median(const Data: array of Double) : Double;
|
969 |
begin
|
970 |
Result := Median16(Data, High(Data)+1);
|
971 |
end;
|
972 |
|
973 |
function Median16(const Data; NData : Integer) : Double;
|
974 |
var
|
975 |
m : Integer;
|
976 |
begin
|
977 |
if (NData <= 0) then
|
978 |
RaiseStatError(stscStatBadCount);
|
979 |
|
980 |
m := NData shr 1;
|
981 |
if odd(NData) then
|
982 |
Result := Largest16(Data, NData, m+1)
|
983 |
else
|
984 |
Result := (Largest16(Data, NData, m+1)+Largest16(Data, NData, m))/2.0;
|
985 |
end;
|
986 |
|
987 |
function Mode(const Data: array of Double) : Double;
|
988 |
begin
|
989 |
Result := Mode16(Data, High(Data)+1);
|
990 |
end;
|
991 |
|
992 |
function Mode16(const Data; NData : Integer) : Double;
|
993 |
var
|
994 |
maxf, i, f : Integer;
|
995 |
Size : Cardinal;
|
996 |
last, max : Double;
|
997 |
SD : PDoubleArray;
|
998 |
begin
|
999 |
if (NData <= 0) then
|
1000 |
RaiseStatError(stscStatBadCount);
|
1001 |
|
1002 |
{copy and sort array}
|
1003 |
Size := CopyAndSort(Data, NData, SD);
|
1004 |
try
|
1005 |
{find the value with highest frequency}
|
1006 |
last := SD^[0];
|
1007 |
max := last;
|
1008 |
f := 1;
|
1009 |
maxf := f;
|
1010 |
|
1011 |
for i := 1 to NData-1 do begin
|
1012 |
if SD^[i] = last then
|
1013 |
{keep count of identical values}
|
1014 |
inc(f)
|
1015 |
else begin
|
1016 |
{start a new series}
|
1017 |
if f > maxf then begin
|
1018 |
max := last;
|
1019 |
maxf := f;
|
1020 |
end;
|
1021 |
last := SD^[i];
|
1022 |
f := 1;
|
1023 |
end;
|
1024 |
end;
|
1025 |
|
1026 |
{test last group}
|
1027 |
if f > maxf then
|
1028 |
max := last;
|
1029 |
|
1030 |
Result := max;
|
1031 |
finally
|
1032 |
freemem(SD, Size);
|
1033 |
end;
|
1034 |
end;
|
1035 |
|
1036 |
function Percentile(const Data: array of Double; K : Double) : Double;
|
1037 |
begin
|
1038 |
Result := Percentile16(Data, High(Data)+1, K);
|
1039 |
end;
|
1040 |
|
1041 |
function Percentile16(const Data; NData : Integer; K : Double) : Double;
|
1042 |
const
|
1043 |
eps = 1.0e-10;
|
1044 |
var
|
1045 |
ibin : Integer;
|
1046 |
Size : Cardinal;
|
1047 |
rbin, l, h : Double;
|
1048 |
SD : PDoubleArray;
|
1049 |
begin
|
1050 |
if (NData <= 0) then
|
1051 |
RaiseStatError(stscStatBadCount);
|
1052 |
if (K < 0.0) or (K > 1.0) then
|
1053 |
RaiseStatError(stscStatBadParam);
|
1054 |
|
1055 |
{copy and sort array}
|
1056 |
Size := CopyAndSort(Data, NData, SD);
|
1057 |
try
|
1058 |
{find nearest bins}
|
1059 |
rbin := K*(NData-1);
|
1060 |
ibin := Trunc(rbin);
|
1061 |
if Frac(rbin) < eps then
|
1062 |
{very close to array index below}
|
1063 |
Result := SD^[ibin]
|
1064 |
else if (Int(rbin)+1.0-rbin) < eps then
|
1065 |
{very close to array index above}
|
1066 |
Result := SD^[ibin+1]
|
1067 |
else begin
|
1068 |
{need to interpolate between two bins}
|
1069 |
l := SD^[ibin];
|
1070 |
h := SD^[ibin+1];
|
1071 |
Result := l+(h-l)*(K*(NData-1)-ibin);
|
1072 |
end;
|
1073 |
finally
|
1074 |
freemem(SD, Size);
|
1075 |
end;
|
1076 |
end;
|
1077 |
|
1078 |
function PercentRank(const Data: array of Double; X : Double) : Double;
|
1079 |
begin
|
1080 |
Result := PercentRank16(Data, High(Data)+1, X);
|
1081 |
end;
|
1082 |
|
1083 |
function PercentRank16(const Data; NData : Integer; X : Double) : Double;
|
1084 |
var
|
1085 |
b, t, m : Integer;
|
1086 |
Size : Cardinal;
|
1087 |
SD : PDoubleArray;
|
1088 |
begin
|
1089 |
if (NData <= 0) then
|
1090 |
RaiseStatError(stscStatBadCount);
|
1091 |
|
1092 |
{copy and sort array}
|
1093 |
Size := CopyAndSort(Data, NData, SD);
|
1094 |
try
|
1095 |
{test end conditions}
|
1096 |
if (X < SD^[0]) or (X > SD^[NData-1]) then
|
1097 |
RaiseStatError(stscStatBadParam);
|
1098 |
|
1099 |
{find nearby bins using binary search}
|
1100 |
b := 0;
|
1101 |
t := NData-1;
|
1102 |
while (t-b) > 1 do begin
|
1103 |
m := (b+t) shr 1;
|
1104 |
if (X >= SD^[m]) then
|
1105 |
{search upper half}
|
1106 |
b := m
|
1107 |
else
|
1108 |
{search lower half}
|
1109 |
t := m;
|
1110 |
end;
|
1111 |
|
1112 |
{now X is known to be between b (inclusive) and b+1}
|
1113 |
{handle duplicate elements below b}
|
1114 |
while (b > 0) and (SD^[b-1] = X) do
|
1115 |
dec(b);
|
1116 |
|
1117 |
if (SD^[b] = X) then
|
1118 |
{an exact match}
|
1119 |
Result := b/(NData-1)
|
1120 |
else
|
1121 |
{interpolate}
|
1122 |
Result := (b+(X-SD^[b])/(SD^[b+1]-SD^[b]))/(NData-1);
|
1123 |
|
1124 |
finally
|
1125 |
freemem(SD, Size);
|
1126 |
end;
|
1127 |
end;
|
1128 |
|
1129 |
const
|
1130 |
sqrt2pi = 2.5066282746310005; {sqrt(2*pi)}
|
1131 |
|
1132 |
function GammaLn(X : Single) : Single;
|
1133 |
{-Returns ln(Gamma(X)) where X > 0}
|
1134 |
const
|
1135 |
cof : array[0..5] of Double = (
|
1136 |
76.18009172947146, -86.50532032941677, 24.01409824083091,
|
1137 |
-1.231739572450155, 0.1208650973866179e-2, -0.5395239384953e-5);
|
1138 |
var
|
1139 |
y, tmp, ser : Double;
|
1140 |
j : Integer;
|
1141 |
begin
|
1142 |
if (X <= 0) then
|
1143 |
RaiseStatError(stscStatBadParam);
|
1144 |
|
1145 |
y := X;
|
1146 |
tmp := X+5.5;
|
1147 |
tmp := tmp-(X+0.5)*ln(tmp);
|
1148 |
ser := 1.000000000190015;
|
1149 |
for j := low(cof) to high(cof) do begin
|
1150 |
y := y+1.0;
|
1151 |
ser := ser+cof[j]/y;
|
1152 |
end;
|
1153 |
Result := -tmp+ln(sqrt2pi*ser/X);
|
1154 |
end;
|
1155 |
|
1156 |
const
|
1157 |
MFactLnA = 65;
|
1158 |
var
|
1159 |
FactLnA : array[2..MFactLna] of Single; {lookup table of FactLn values}
|
1160 |
|
1161 |
function FactLn(N : Integer) : Single;
|
1162 |
{-Returns ln(N!) for N >= 0}
|
1163 |
begin
|
1164 |
if (N <= 1) then
|
1165 |
Result := 0.0
|
1166 |
else if (N <= MFactLnA) then
|
1167 |
{use lookup table}
|
1168 |
Result := FactLnA[N]
|
1169 |
else
|
1170 |
{compute each time}
|
1171 |
Result := GammaLn(N+1.0);
|
1172 |
end;
|
1173 |
|
1174 |
const
|
1175 |
MFactA = 33;
|
1176 |
var
|
1177 |
FactA : array[2..MFactA] of Double; {lookup table of factorial values}
|
1178 |
|
1179 |
function Factorial(N : Integer) : Extended;
|
1180 |
begin
|
1181 |
if (N < 0) then
|
1182 |
RaiseStatError(stscStatBadParam);
|
1183 |
|
1184 |
if (N <= 1) then
|
1185 |
Result := 1.0
|
1186 |
else if (N <= MFactA) then
|
1187 |
{use lookup table}
|
1188 |
Result := FactA[N]
|
1189 |
else
|
1190 |
{bigger than lookup table allows. may overflow!}
|
1191 |
Result := exp(GammaLn(N+1.0))
|
1192 |
end;
|
1193 |
|
1194 |
function Permutations(Number, NumberChosen : Integer) : Extended;
|
1195 |
begin
|
1196 |
if (Number < 0) or (NumberChosen < 0) or (Number < NumberChosen) then
|
1197 |
RaiseStatError(stscStatBadParam);
|
1198 |
{the 0.5 and Int function clean up roundoff error for smaller N and K}
|
1199 |
Result := Int(0.5+exp(FactLn(Number)-FactLn(Number-NumberChosen)));
|
1200 |
end;
|
1201 |
|
1202 |
function Combinations(Number, NumberChosen : Integer) : Extended;
|
1203 |
begin
|
1204 |
if (Number < 0) or (NumberChosen < 0) or (Number < NumberChosen) then
|
1205 |
RaiseStatError(stscStatBadParam);
|
1206 |
{the 0.5 and Int function clean up roundoff error for smaller N and K}
|
1207 |
Result := Int(0.5+exp(FactLn(Number)-FactLn(NumberChosen)
|
1208 |
-FactLn(Number-NumberChosen)));
|
1209 |
end;
|
1210 |
|
1211 |
function Rank(Number: Double; const Data: array of Double;
|
1212 |
Ascending: Boolean) : Integer;
|
1213 |
begin
|
1214 |
Result := Rank16(Number, Data, High(Data)+1, Ascending);
|
1215 |
end;
|
1216 |
|
1217 |
function Rank16(Number: Double; const Data; NData : Integer;
|
1218 |
Ascending: Boolean) : Integer;
|
1219 |
var
|
1220 |
r : Integer;
|
1221 |
begin
|
1222 |
if (NData <= 0) then
|
1223 |
RaiseStatError(stscStatBadCount);
|
1224 |
|
1225 |
{Data not known to be sorted, so must search linearly}
|
1226 |
if (Ascending) then begin
|
1227 |
for r := 0 to NData-1 do
|
1228 |
if TDoubleArray(Data)[r] = Number then begin
|
1229 |
Result := r+1;
|
1230 |
exit;
|
1231 |
end;
|
1232 |
end else begin
|
1233 |
for r := NData-1 downto 0 do
|
1234 |
if TDoubleArray(Data)[r] = Number then begin
|
1235 |
Result := NData-r;
|
1236 |
exit;
|
1237 |
end;
|
1238 |
end;
|
1239 |
Result := 0;
|
1240 |
end;
|
1241 |
|
1242 |
function Smallest(const Data: array of Double; K : Integer) : Double;
|
1243 |
begin
|
1244 |
Result := Smallest16(Data, High(Data)+1, K);
|
1245 |
end;
|
1246 |
|
1247 |
function Smallest16(const Data; NData : Integer; K : Integer) : Double;
|
1248 |
var
|
1249 |
b, t, i, j : integer;
|
1250 |
Size : LongInt;
|
1251 |
temp, pval : Double;
|
1252 |
SD : PDoubleArray;
|
1253 |
begin
|
1254 |
if (NData <= 0) then
|
1255 |
RaiseStatError(stscStatBadCount);
|
1256 |
if (K <= 0) or (K > NData) then
|
1257 |
RaiseStatError(stscStatBadParam);
|
1258 |
|
1259 |
Size := LongInt(NData)*sizeof(Double);
|
1260 |
{if (Size > MaxBlockSize) then}
|
1261 |
{ RaiseStatError(stscStatBadCount);}
|
1262 |
getmem(SD, Size); {raises exception if insufficient memory}
|
1263 |
try
|
1264 |
move(Data, SD^, Size);
|
1265 |
|
1266 |
{make K 0-based}
|
1267 |
dec(K);
|
1268 |
{use quicksort-like selection}
|
1269 |
b := 0;
|
1270 |
t := NData-1;
|
1271 |
while (t > b) do begin
|
1272 |
{use random pivot in case of already-sorted data}
|
1273 |
pval := SD^[b+random(t-b+1)];
|
1274 |
i := b;
|
1275 |
j := t;
|
1276 |
repeat
|
1277 |
while (SD^[i] < pval) do
|
1278 |
inc(i);
|
1279 |
while (pval < SD^[j]) do
|
1280 |
dec(j);
|
1281 |
if (i <= j) then begin
|
1282 |
temp := SD^[i];
|
1283 |
SD^[i] := SD^[j];
|
1284 |
SD^[j] := temp;
|
1285 |
inc(i);
|
1286 |
dec(j);
|
1287 |
end;
|
1288 |
until (i > j);
|
1289 |
|
1290 |
if (j < K) then
|
1291 |
b := i;
|
1292 |
if (K < i) then
|
1293 |
t := j;
|
1294 |
end;
|
1295 |
Result := SD^[K];
|
1296 |
finally
|
1297 |
freemem(SD, Size);
|
1298 |
end;
|
1299 |
end;
|
1300 |
|
1301 |
{debug version of Smallest: slower but simpler}
|
1302 |
{$IFDEF Debug}
|
1303 |
function SmallestSort(const Data: array of double; K : Integer) : Double;
|
1304 |
var
|
1305 |
Size : Cardinal;
|
1306 |
NData : Integer;
|
1307 |
SD : PDoubleArray;
|
1308 |
begin
|
1309 |
NData := High(Data)+1;
|
1310 |
if (NData <= 0) then
|
1311 |
RaiseStatError(stscStatBadCount);
|
1312 |
if (K <= 0) or (K > NData) then
|
1313 |
RaiseStatError(stscStatBadParam);
|
1314 |
|
1315 |
{copy and sort array}
|
1316 |
Size := CopyAndSort(Data, NData, SD);
|
1317 |
try
|
1318 |
{K=1 returns smallest value, K=NData returns largest}
|
1319 |
Result := SD^[K-1];
|
1320 |
finally
|
1321 |
freemem(SD, Size);
|
1322 |
end;
|
1323 |
end;
|
1324 |
{$ENDIF}
|
1325 |
|
1326 |
function TrimMean(const Data: array of Double; Percent : Double) : Double;
|
1327 |
begin
|
1328 |
Result := TrimMean16(Data, High(Data)+1, Percent);
|
1329 |
end;
|
1330 |
|
1331 |
function TrimMean16(const Data; NData : Integer; Percent : Double) : Double;
|
1332 |
var
|
1333 |
ntrim : Integer;
|
1334 |
Size : Cardinal;
|
1335 |
SD : PDoubleArray;
|
1336 |
begin
|
1337 |
if (NData <= 0) then
|
1338 |
RaiseStatError(stscStatBadCount);
|
1339 |
if (Percent < 0.0) or (Percent > 1.0) then
|
1340 |
RaiseStatError(stscStatBadParam);
|
1341 |
|
1342 |
{compute total number of trimmed points, rounding down to an even number}
|
1343 |
ntrim := trunc(Percent*NData);
|
1344 |
if odd(ntrim) then
|
1345 |
dec(ntrim);
|
1346 |
|
1347 |
{take the easy way out when possible}
|
1348 |
if (ntrim = 0) then begin
|
1349 |
Result := Mean(Data, NData);
|
1350 |
exit;
|
1351 |
end;
|
1352 |
|
1353 |
{copy and sort array}
|
1354 |
Size := CopyAndSort(Data, NData, SD);
|
1355 |
try
|
1356 |
{return Mean of remaining data points}
|
1357 |
Result := Mean(SD^[ntrim shr 1], NData-ntrim);
|
1358 |
finally
|
1359 |
freemem(SD, Size);
|
1360 |
end;
|
1361 |
end;
|
1362 |
|
1363 |
{------------------------------------------------------------------------}
|
1364 |
|
1365 |
procedure LinEst(const KnownY: array of Double;
|
1366 |
const KnownX: array of Double; var LF : TStLinEst; ErrorStats : Boolean);
|
1367 |
begin
|
1368 |
if (High(KnownY) <> High(KnownX)) then
|
1369 |
RaiseStatError(stscStatBadCount);
|
1370 |
LinEst16(KnownY, KnownX, High(KnownY)+1, LF, ErrorStats);
|
1371 |
end;
|
1372 |
|
1373 |
procedure LinEst16(const KnownY; const KnownX; NData : Integer;
|
1374 |
var LF : TStLinEst; ErrorStats : Boolean);
|
1375 |
var
|
1376 |
i : Integer;
|
1377 |
sx, sy, xmean, ymean, sxx, sxy, syy, x, y : Extended;
|
1378 |
begin
|
1379 |
if (NData <= 2) then
|
1380 |
RaiseStatError(stscStatBadCount);
|
1381 |
|
1382 |
{compute basic sums}
|
1383 |
sx := 0.0;
|
1384 |
sy := 0.0;
|
1385 |
sxx := 0.0;
|
1386 |
sxy := 0.0;
|
1387 |
syy := 0.0;
|
1388 |
for i := 0 to NData-1 do begin
|
1389 |
x := TDoubleArray(KnownX)[i];
|
1390 |
y := TDoubleArray(KnownY)[i];
|
1391 |
sx := sx+x;
|
1392 |
sy := sy+y;
|
1393 |
sxx := sxx+x*x;
|
1394 |
syy := syy+y*y;
|
1395 |
sxy := sxy+x*y;
|
1396 |
end;
|
1397 |
xmean := sx/NData;
|
1398 |
ymean := sy/NData;
|
1399 |
sxx := sxx-NData*xmean*xmean;
|
1400 |
syy := syy-NData*ymean*ymean;
|
1401 |
sxy := sxy-NData*xmean*ymean;
|
1402 |
|
1403 |
{check for zero variance}
|
1404 |
if (sxx <= 0.0) or (syy <= 0.0) then
|
1405 |
RaiseStatError(stscStatBadData);
|
1406 |
|
1407 |
{initialize returned parameters}
|
1408 |
fillchar(LF, sizeof(LF), 0);
|
1409 |
|
1410 |
{regression coefficients}
|
1411 |
LF.B1 := sxy/sxx;
|
1412 |
LF.B0 := ymean-LF.B1*xmean;
|
1413 |
|
1414 |
{error statistics}
|
1415 |
if (ErrorStats) then begin
|
1416 |
LF.ssr := LF.B1*sxy;
|
1417 |
LF.sse := syy-LF.ssr;
|
1418 |
LF.R2 := LF.ssr/syy;
|
1419 |
LF.df := NData-2;
|
1420 |
LF.sigma := sqrt(LF.sse/LF.df);
|
1421 |
if LF.sse = 0.0 then
|
1422 |
{pick an arbitrarily large number for perfect fit}
|
1423 |
LF.F0 := 1.7e+308
|
1424 |
else
|
1425 |
LF.F0 := (LF.ssr*LF.df)/LF.sse;
|
1426 |
LF.seB1 := LF.sigma/sqrt(sxx);
|
1427 |
LF.seB0 := LF.sigma*sqrt((1.0/NData)+(xmean*xmean/sxx));
|
1428 |
end;
|
1429 |
end;
|
1430 |
|
1431 |
procedure LogEst(const KnownY: array of Double;
|
1432 |
const KnownX: array of Double; var LF : TStLinEst; ErrorStats : Boolean);
|
1433 |
begin
|
1434 |
if (High(KnownY) <> High(KnownX)) then
|
1435 |
RaiseStatError(stscStatBadCount);
|
1436 |
LogEst16(KnownY, KnownX, High(KnownY)+1, LF, ErrorStats);
|
1437 |
end;
|
1438 |
|
1439 |
procedure LogEst16(const KnownY; const KnownX; NData : Integer;
|
1440 |
var LF : TStLinEst; ErrorStats : Boolean);
|
1441 |
var
|
1442 |
i : Integer;
|
1443 |
Size : LongInt;
|
1444 |
lny : PDoubleArray;
|
1445 |
begin
|
1446 |
if (NData <= 2) then
|
1447 |
RaiseStatError(stscStatBadCount);
|
1448 |
|
1449 |
{allocate array for the log-transformed data}
|
1450 |
Size := LongInt(NData)*sizeof(Double);
|
1451 |
{f (Size > MaxBlockSize) then}
|
1452 |
{ RaiseStatError(stscStatBadCount);}
|
1453 |
getmem(lny, Size);
|
1454 |
try
|
1455 |
{initialize transformed data}
|
1456 |
for i := 0 to NData-1 do
|
1457 |
lny^[i] := ln(TDoubleArray(KnownY)[i]);
|
1458 |
|
1459 |
{fit transformed data}
|
1460 |
LinEst16(lny^, KnownX, NData, LF, ErrorStats);
|
1461 |
|
1462 |
{return values for B0 and B1 in exponential model y=B0*B1^x}
|
1463 |
LF.B0 := exp(LF.B0);
|
1464 |
LF.B1 := exp(LF.B1);
|
1465 |
{leave other values in LF in log form}
|
1466 |
finally
|
1467 |
freemem(lny, Size);
|
1468 |
end;
|
1469 |
end;
|
1470 |
|
1471 |
function Forecast(X : Double; const KnownY: array of Double;
|
1472 |
const KnownX: array of Double) : Double;
|
1473 |
begin
|
1474 |
if (High(KnownY) <> High(KnownX)) then
|
1475 |
RaiseStatError(stscStatBadCount);
|
1476 |
Result := Forecast16(X, KnownY, KnownX, High(KnownY)+1);
|
1477 |
end;
|
1478 |
|
1479 |
function Forecast16(X : Double; const KnownY; const KnownX;
|
1480 |
NData : Integer) : Double;
|
1481 |
var
|
1482 |
LF : TStLinEst;
|
1483 |
begin
|
1484 |
LinEst16(KnownY, KnownX, NData, LF, false);
|
1485 |
Result := LF.B0+LF.B1*X;
|
1486 |
end;
|
1487 |
|
1488 |
function ForecastExponential(X : Double; const KnownY: array of Double;
|
1489 |
const KnownX: array of Double) : Double;
|
1490 |
begin
|
1491 |
if (High(KnownY) <> High(KnownX)) then
|
1492 |
RaiseStatError(stscStatBadCount);
|
1493 |
Result := ForecastExponential16(X, KnownY, KnownX, High(KnownY)+1);
|
1494 |
end;
|
1495 |
|
1496 |
function ForecastExponential16(X : Double; const KnownY; const KnownX;
|
1497 |
NData : Integer) : Double;
|
1498 |
var
|
1499 |
LF : TStLinEst;
|
1500 |
begin
|
1501 |
LogEst16(KnownY, KnownX, NData, LF, false);
|
1502 |
Result := LF.B0*Power(LF.B1, X);
|
1503 |
end;
|
1504 |
|
1505 |
function Intercept(const KnownY: array of Double;
|
1506 |
const KnownX: array of Double) : Double;
|
1507 |
begin
|
1508 |
if (High(KnownY) <> High(KnownX)) then
|
1509 |
RaiseStatError(stscStatBadCount);
|
1510 |
Result := Intercept16(KnownY, KnownX, High(KnownY)+1);
|
1511 |
end;
|
1512 |
|
1513 |
function Intercept16(const KnownY; const KnownX; NData : Integer) : Double;
|
1514 |
var
|
1515 |
LF : TStLinEst;
|
1516 |
begin
|
1517 |
LinEst16(KnownY, KnownX, NData, LF, false);
|
1518 |
Result := LF.B0;
|
1519 |
end;
|
1520 |
|
1521 |
function RSquared(const KnownY: array of Double;
|
1522 |
const KnownX: array of Double) : Double;
|
1523 |
begin
|
1524 |
if (High(KnownY) <> High(KnownX)) then
|
1525 |
RaiseStatError(stscStatBadCount);
|
1526 |
Result := RSquared16(KnownY, KnownX, High(KnownY)+1);
|
1527 |
end;
|
1528 |
|
1529 |
function RSquared16(const KnownY; const KnownX; NData : Integer) : Double;
|
1530 |
var
|
1531 |
LF : TStLinEst;
|
1532 |
begin
|
1533 |
LinEst16(KnownY, KnownX, NData, LF, true);
|
1534 |
Result := LF.R2;
|
1535 |
end;
|
1536 |
|
1537 |
function Slope(const KnownY: array of Double;
|
1538 |
const KnownX: array of Double) : Double;
|
1539 |
begin
|
1540 |
if (High(KnownY) <> High(KnownX)) then
|
1541 |
RaiseStatError(stscStatBadCount);
|
1542 |
Result := Slope16(KnownY, KnownX, High(KnownY)+1);
|
1543 |
end;
|
1544 |
|
1545 |
function Slope16(const KnownY; const KnownX; NData : Integer) : Double;
|
1546 |
var
|
1547 |
LF : TStLinEst;
|
1548 |
begin
|
1549 |
LinEst16(KnownY, KnownX, NData, LF, false);
|
1550 |
Result := LF.B1;
|
1551 |
end;
|
1552 |
|
1553 |
function StandardErrorY(const KnownY: array of Double;
|
1554 |
const KnownX: array of Double) : Double;
|
1555 |
begin
|
1556 |
if (High(KnownY) <> High(KnownX)) then
|
1557 |
RaiseStatError(stscStatBadCount);
|
1558 |
Result := StandardErrorY16(KnownY, KnownX, High(KnownY)+1);
|
1559 |
end;
|
1560 |
|
1561 |
function StandardErrorY16(const KnownY; const KnownX;
|
1562 |
NData : Integer) : Double;
|
1563 |
var
|
1564 |
LF : TStLinEst;
|
1565 |
begin
|
1566 |
LinEst16(KnownY, KnownX, NData, LF, true);
|
1567 |
Result := LF.sigma;
|
1568 |
end;
|
1569 |
|
1570 |
{------------------------------------------------------------------------}
|
1571 |
|
1572 |
function BetaCf(a, b, x : Single) : Single;
|
1573 |
{-Evaluates continued fraction for incomplete beta function}
|
1574 |
const
|
1575 |
MAXIT = 100;
|
1576 |
EPS = 3.0E-7;
|
1577 |
FPMIN = 1.0E-30;
|
1578 |
var
|
1579 |
m, m2 : Integer;
|
1580 |
aa, c, d, del, h, qab, qam, qap : Double;
|
1581 |
begin
|
1582 |
qab := a+b;
|
1583 |
qap := a+1.0;
|
1584 |
qam := a-1.0;
|
1585 |
c := 1.0;
|
1586 |
d := 1.0-qab*x/qap;
|
1587 |
if (abs(d) < FPMIN) then
|
1588 |
d := FPMIN;
|
1589 |
d := 1.0/d;
|
1590 |
h := d;
|
1591 |
for m := 1 to MAXIT do begin
|
1592 |
m2 := 2*m;
|
1593 |
aa := m*(b-m)*x/((qam+m2)*(a+m2));
|
1594 |
d := 1.0+aa*d;
|
1595 |
if (abs(d) < FPMIN) then
|
1596 |
d := FPMIN;
|
1597 |
c := 1.0+aa/c;
|
1598 |
if (abs(c) < FPMIN) then
|
1599 |
c := FPMIN;
|
1600 |
d := 1.0/d;
|
1601 |
h := h*d*c;
|
1602 |
aa := -(a+m)*(qab+m)*x/((a+m2)*(qap+m2));
|
1603 |
|
1604 |
d := 1.0+aa*d;
|
1605 |
if (abs(d) < FPMIN) then
|
1606 |
d := FPMIN;
|
1607 |
c := 1.0+aa/c;
|
1608 |
if (abs(c) < FPMIN) then
|
1609 |
c := FPMIN;
|
1610 |
d := 1.0/d;
|
1611 |
del := d*c;
|
1612 |
h := h*del;
|
1613 |
|
1614 |
{check for convergence}
|
1615 |
if (abs(del-1.0) < EPS) then
|
1616 |
break;
|
1617 |
if m = MAXIT then
|
1618 |
RaiseStatError(stscStatNoConverge);
|
1619 |
end;
|
1620 |
Result := h;
|
1621 |
end;
|
1622 |
|
1623 |
function BetaDist(X, Alpha, Beta, A, B : Single) : Single;
|
1624 |
var
|
1625 |
bt : Double;
|
1626 |
begin
|
1627 |
if (X < A) or (X > B) or (A = B) or (Alpha <= 0.0) or (Beta <= 0.0) then
|
1628 |
RaiseStatError(stscStatBadParam);
|
1629 |
|
1630 |
{normalize X}
|
1631 |
X := (X-A)/(B-A);
|
1632 |
|
1633 |
{compute factors in front of continued fraction expansion}
|
1634 |
if (X = 0.0) or (X = 1.0) then
|
1635 |
bt := 0.0
|
1636 |
else
|
1637 |
bt := exp(GammaLn(Alpha+Beta)-GammaLn(Alpha)-GammaLn(Beta)+
|
1638 |
Alpha*ln(X)+Beta*ln(1.0-X));
|
1639 |
|
1640 |
{use symmetry relationship to make continued fraction converge quickly}
|
1641 |
if (X < (Alpha+1.0)/(Alpha+Beta+2.0)) then
|
1642 |
Result := bt*BetaCf(Alpha, Beta, X)/Alpha
|
1643 |
else
|
1644 |
Result := 1.0-bt*BetaCf(Beta, Alpha, 1.0-X)/Beta;
|
1645 |
end;
|
1646 |
|
1647 |
function Sign(a, b : Double) : Double;
|
1648 |
{-Returns abs(a) if b >= 0.0, else -abs(a)}
|
1649 |
begin
|
1650 |
if (b >= 0.0) then
|
1651 |
Result := abs(a)
|
1652 |
else
|
1653 |
Result := -abs(a);
|
1654 |
end;
|
1655 |
|
1656 |
function BetaInv(Probability, Alpha, Beta, A, B : Single) : Single;
|
1657 |
const
|
1658 |
MAXIT = 100;
|
1659 |
UNUSED = -1.11e30;
|
1660 |
XACC = 3e-7;
|
1661 |
var
|
1662 |
j : Integer;
|
1663 |
ans, fh, fl, fm, fnew, s, xh, xl, xm, xnew, dsign : Double;
|
1664 |
begin
|
1665 |
if (Probability < 0.0) or (Probability > 1.0) or
|
1666 |
(A = B) or (Alpha <= 0.0) or (Beta <= 0.0) then
|
1667 |
RaiseStatError(stscStatBadParam);
|
1668 |
|
1669 |
if (Probability = 0.0) then
|
1670 |
Result := A
|
1671 |
else if (Probability = 1.0) then
|
1672 |
Result := B
|
1673 |
else begin
|
1674 |
{Ridder's method of finding the root of BetaDist = Probability}
|
1675 |
fl := -Probability; {BetaDist(A, Alpha, Beta, A, B)-Probability}
|
1676 |
fh := 1.0-Probability; {BetaDist(B, Alpha, Beta, A, B)-Probability}
|
1677 |
xl := A;
|
1678 |
xh := B;
|
1679 |
ans := UNUSED;
|
1680 |
|
1681 |
for j := 1 to MAXIT do begin
|
1682 |
xm := 0.5*(xl+xh);
|
1683 |
fm := BetaDist(xm, Alpha, Beta, A, B)-Probability;
|
1684 |
s := sqrt(fm*fm-fl*fh);
|
1685 |
if (s = 0.0) then begin
|
1686 |
Result := ans;
|
1687 |
exit;
|
1688 |
end;
|
1689 |
if (fl >= fh) then
|
1690 |
dsign := 1.0
|
1691 |
else
|
1692 |
dsign := -1.0;
|
1693 |
xnew := xm+(xm-xl)*(dsign*fm/s);
|
1694 |
if (abs(xnew-ans) <= XACC) then begin
|
1695 |
Result := ans;
|
1696 |
exit;
|
1697 |
end;
|
1698 |
ans := xnew;
|
1699 |
|
1700 |
fnew := BetaDist(ans, Alpha, Beta, A, B)-Probability;
|
1701 |
if (fnew = 0.0) then begin
|
1702 |
Result := ans;
|
1703 |
exit;
|
1704 |
end;
|
1705 |
|
1706 |
{keep root bracketed on next iteration}
|
1707 |
if (Sign(fm, fnew) <> fm) then begin
|
1708 |
xl := xm;
|
1709 |
fl := fm;
|
1710 |
xh := ans;
|
1711 |
fh := fnew;
|
1712 |
end else if (Sign(fl, fnew) <> fl) then begin
|
1713 |
xh := ans;
|
1714 |
fh := fnew;
|
1715 |
end else if (Sign(fh, fnew) <> fh) then begin
|
1716 |
xl := ans;
|
1717 |
fl := fnew;
|
1718 |
end else
|
1719 |
{shouldn't get here}
|
1720 |
RaiseStatError(stscStatNoConverge);
|
1721 |
|
1722 |
if (abs(xh-xl) <= XACC) then begin
|
1723 |
Result := ans;
|
1724 |
exit;
|
1725 |
end;
|
1726 |
end;
|
1727 |
BetaInv := A; {avoid compiler warning}
|
1728 |
RaiseStatError(stscStatNoConverge);
|
1729 |
end;
|
1730 |
end;
|
1731 |
|
1732 |
function BinomDistPmf(N, K : Integer; p : Extended) : Double;
|
1733 |
{-Returns the Probability mass function of the binomial distribution}
|
1734 |
begin
|
1735 |
Result := Combinations(N, K)*IntPower(p, K)*IntPower(1.0-p, N-K);
|
1736 |
end;
|
1737 |
|
1738 |
function BinomDist(NumberS, Trials : Integer; ProbabilityS : Single;
|
1739 |
Cumulative : Boolean) : Single;
|
1740 |
begin
|
1741 |
if (Trials < 0) or (NumberS < 0) or (NumberS > Trials) or
|
1742 |
(ProbabilityS < 0.0) or (ProbabilityS > 1.0) then
|
1743 |
RaiseStatError(stscStatBadParam);
|
1744 |
|
1745 |
if (Cumulative) then
|
1746 |
Result := 1.0+BinomDistPmf(Trials, NumberS, ProbabilityS)-
|
1747 |
BetaDist(ProbabilityS, NumberS, Trials-NumberS+1, 0.0, 1.0)
|
1748 |
else
|
1749 |
Result := BinomDistPmf(Trials, NumberS, ProbabilityS);
|
1750 |
end;
|
1751 |
|
1752 |
function CritBinom(Trials : Integer; ProbabilityS, Alpha : Single) : Integer;
|
1753 |
var
|
1754 |
s : Integer;
|
1755 |
B : Double;
|
1756 |
begin
|
1757 |
if (Trials < 0) or (ProbabilityS < 0.0) or (ProbabilityS > 1.0) or
|
1758 |
(Alpha < 0.0) or (Alpha > 1.0) then
|
1759 |
RaiseStatError(stscStatBadParam);
|
1760 |
|
1761 |
B := 0.0;
|
1762 |
for s := 0 to Trials do begin
|
1763 |
B := B+BinomDistPmf(Trials, s, ProbabilityS);
|
1764 |
if (B >= Alpha) then begin
|
1765 |
Result := s;
|
1766 |
exit;
|
1767 |
end;
|
1768 |
end;
|
1769 |
{in case of roundoff problems}
|
1770 |
Result := Trials;
|
1771 |
end;
|
1772 |
|
1773 |
function GammSer(a, x : Single) : Single;
|
1774 |
{-Returns the series computation for GammP}
|
1775 |
const
|
1776 |
MAXIT = 100;
|
1777 |
EPS = 3.0E-7;
|
1778 |
var
|
1779 |
N : Integer;
|
1780 |
sum, del, ap : Double;
|
1781 |
begin
|
1782 |
Result := 0.0;
|
1783 |
if (x > 0.0) then begin
|
1784 |
{x shouldn't be < 0.0, tested by caller}
|
1785 |
ap := a;
|
1786 |
sum := 1.0/a;
|
1787 |
del := sum;
|
1788 |
for N := 1 to MAXIT do begin
|
1789 |
ap := ap+1;
|
1790 |
del := del*x/ap;
|
1791 |
sum := sum+del;
|
1792 |
if (abs(del) < abs(sum)*EPS) then begin
|
1793 |
Result := sum*exp(-X+a*ln(X)-GammaLn(a));
|
1794 |
exit;
|
1795 |
end;
|
1796 |
end;
|
1797 |
RaiseStatError(stscStatNoConverge);
|
1798 |
end;
|
1799 |
end;
|
1800 |
|
1801 |
function GammCf(a, x : Single) : Single;
|
1802 |
{-Returns the continued fraction computation for GammP}
|
1803 |
const
|
1804 |
MAXIT = 100;
|
1805 |
EPS = 3.0e-7;
|
1806 |
FPMIN = 1.0e-30;
|
1807 |
var
|
1808 |
i : Integer;
|
1809 |
an, b, c, d, del, h : Double;
|
1810 |
begin
|
1811 |
b := x+1.0-a;
|
1812 |
c := 1.0/FPMIN;
|
1813 |
d := 1.0/b;
|
1814 |
h := d;
|
1815 |
for i := 1 to MAXIT do begin
|
1816 |
an := -i*(i-a);
|
1817 |
b := b+2.0;
|
1818 |
d := an*d+b;
|
1819 |
if (abs(d) < FPMIN) then
|
1820 |
d := FPMIN;
|
1821 |
c := b+an/c;
|
1822 |
if (abs(c) < FPMIN) then
|
1823 |
c := FPMIN;
|
1824 |
d := 1.0/d;
|
1825 |
del := d*c;
|
1826 |
h := h*del;
|
1827 |
if (abs(del-1.0) < EPS) then
|
1828 |
break;
|
1829 |
if i = MAXIT then
|
1830 |
RaiseStatError(stscStatNoConverge);
|
1831 |
end;
|
1832 |
Result := h*exp(-x+a*ln(x)-GammaLn(a));
|
1833 |
end;
|
1834 |
|
1835 |
function GammP(a, x : Single) : Single;
|
1836 |
{-Returns the incomplete gamma function P(a, x)}
|
1837 |
begin
|
1838 |
if (x < 0.0) or (a <= 0.0) then
|
1839 |
RaiseStatError(stscStatBadParam);
|
1840 |
if (x < a+1.0) then
|
1841 |
{use the series representation}
|
1842 |
Result := GammSer(a, x)
|
1843 |
else
|
1844 |
{use the continued fraction representation}
|
1845 |
Result := 1.0-GammCf(a, x);
|
1846 |
end;
|
1847 |
|
1848 |
function ChiDist(X : Single; DegreesFreedom : Integer) : Single;
|
1849 |
begin
|
1850 |
if (DegreesFreedom < 1) or (X < 0.0) then
|
1851 |
RaiseStatError(stscStatBadParam);
|
1852 |
Result := 1.0-GammP(DegreesFreedom/2.0, X/2.0);
|
1853 |
end;
|
1854 |
|
1855 |
function ChiInv(Probability : Single; DegreesFreedom : Integer) : Single;
|
1856 |
const
|
1857 |
MAXIT = 100;
|
1858 |
UNUSED = -1.11e30;
|
1859 |
XACC = 3e-7;
|
1860 |
FACTOR = 1.6;
|
1861 |
var
|
1862 |
j : Integer;
|
1863 |
ans, fh, fl, fm, fnew, s, xh, xl, xm, xnew, dsign : Double;
|
1864 |
begin
|
1865 |
if (Probability < 0.0) or (Probability > 1.0) or (DegreesFreedom < 1) then
|
1866 |
RaiseStatError(stscStatBadParam);
|
1867 |
|
1868 |
if (Probability = 0.0) then
|
1869 |
Result := 0.0
|
1870 |
else begin
|
1871 |
{bracket the interval}
|
1872 |
xl := 0.0;
|
1873 |
xh := 100.0;
|
1874 |
fl := ChiDist(xl, DegreesFreedom)-Probability;
|
1875 |
fh := ChiDist(xh, DegreesFreedom)-Probability;
|
1876 |
for j := 1 to MAXIT do begin
|
1877 |
if (fl*fh < 0.0) then
|
1878 |
{bracketed the root}
|
1879 |
break;
|
1880 |
if (abs(fl) < abs(fh)) then begin
|
1881 |
xl := xl+FACTOR*(xl-xh);
|
1882 |
fl := ChiDist(xl, DegreesFreedom)-Probability;
|
1883 |
end else begin
|
1884 |
xh := xh+FACTOR*(xh-xl);
|
1885 |
fh := ChiDist(xh, DegreesFreedom)-Probability;
|
1886 |
end;
|
1887 |
end;
|
1888 |
if (fl*fh >= 0.0) then
|
1889 |
{couldn't bracket it, means Probability too close to 1.0}
|
1890 |
RaiseStatError(stscStatNoConverge);
|
1891 |
|
1892 |
{Ridder's method of finding the root of ChiDist = Probability}
|
1893 |
ans := UNUSED;
|
1894 |
|
1895 |
for j := 1 to MAXIT do begin
|
1896 |
xm := 0.5*(xl+xh);
|
1897 |
fm := ChiDist(xm, DegreesFreedom)-Probability;
|
1898 |
s := sqrt(fm*fm-fl*fh);
|
1899 |
if (s = 0.0) then begin
|
1900 |
Result := ans;
|
1901 |
exit;
|
1902 |
end;
|
1903 |
if (fl >= fh) then
|
1904 |
dsign := 1.0
|
1905 |
else
|
1906 |
dsign := -1.0;
|
1907 |
xnew := xm+(xm-xl)*(dsign*fm/s);
|
1908 |
if (abs(xnew-ans) <= XACC) then begin
|
1909 |
Result := ans;
|
1910 |
exit;
|
1911 |
end;
|
1912 |
ans := xnew;
|
1913 |
|
1914 |
fnew := ChiDist(ans, DegreesFreedom)-Probability;
|
1915 |
if (fnew = 0.0) then begin
|
1916 |
Result := ans;
|
1917 |
exit;
|
1918 |
end;
|
1919 |
|
1920 |
{keep root bracketed on next iteration}
|
1921 |
if (Sign(fm, fnew) <> fm) then begin
|
1922 |
xl := xm;
|
1923 |
fl := fm;
|
1924 |
xh := ans;
|
1925 |
fh := fnew;
|
1926 |
end else if (Sign(fl, fnew) <> fl) then begin
|
1927 |
xh := ans;
|
1928 |
fh := fnew;
|
1929 |
end else if (Sign(fh, fnew) <> fh) then begin
|
1930 |
xl := ans;
|
1931 |
fl := fnew;
|
1932 |
end else
|
1933 |
{shouldn't get here}
|
1934 |
RaiseStatError(stscStatNoConverge);
|
1935 |
|
1936 |
if (abs(xh-xl) <= XACC) then begin
|
1937 |
Result := ans;
|
1938 |
exit;
|
1939 |
end;
|
1940 |
end;
|
1941 |
Result := 0.0; {avoid compiler warning}
|
1942 |
RaiseStatError(stscStatNoConverge);
|
1943 |
end;
|
1944 |
end;
|
1945 |
|
1946 |
function ExponDist(X, Lambda : Single; Cumulative : Boolean) : Single;
|
1947 |
begin
|
1948 |
if (X < 0.0) or (Lambda <= 0.0) then
|
1949 |
RaiseStatError(stscStatBadParam);
|
1950 |
|
1951 |
if (Cumulative) then
|
1952 |
Result := 1.0-exp(-Lambda*X)
|
1953 |
else
|
1954 |
Result := Lambda*exp(-Lambda*X);
|
1955 |
end;
|
1956 |
|
1957 |
function FDist(X : Single;
|
1958 |
DegreesFreedom1, DegreesFreedom2 : Integer) : Single;
|
1959 |
begin
|
1960 |
if (X < 0) or (DegreesFreedom1 < 1) or (DegreesFreedom2 < 1) then
|
1961 |
RaiseStatError(stscStatBadParam);
|
1962 |
|
1963 |
Result := BetaDist(DegreesFreedom2/(DegreesFreedom2+DegreesFreedom1*X),
|
1964 |
DegreesFreedom2/2.0, DegreesFreedom1/2.0, 0.0, 1.0);
|
1965 |
end;
|
1966 |
|
1967 |
function FInv(Probability : Single;
|
1968 |
DegreesFreedom1, DegreesFreedom2 : Integer) : Single;
|
1969 |
const
|
1970 |
MAXIT = 100;
|
1971 |
UNUSED = -1.11e30;
|
1972 |
XACC = 3e-7;
|
1973 |
FACTOR = 1.6;
|
1974 |
var
|
1975 |
j : Integer;
|
1976 |
ans, fh, fl, fm, fnew, s, xh, xl, xm, xnew, dsign : Double;
|
1977 |
begin
|
1978 |
if (Probability < 0.0) or (Probability > 1.0) or
|
1979 |
(DegreesFreedom1 < 1) or (DegreesFreedom2 < 1) then
|
1980 |
RaiseStatError(stscStatBadParam);
|
1981 |
|
1982 |
if (Probability = 1.0) then
|
1983 |
Result := 0.0
|
1984 |
else begin
|
1985 |
{bracket the interval}
|
1986 |
xl := 0.0;
|
1987 |
xh := 100.0;
|
1988 |
fl := FDist(xl, DegreesFreedom1, DegreesFreedom2)-Probability;
|
1989 |
fh := FDist(xh, DegreesFreedom1, DegreesFreedom2)-Probability;
|
1990 |
for j := 1 to MAXIT do begin
|
1991 |
if (fl*fh < 0.0) then
|
1992 |
{bracketed the root}
|
1993 |
break;
|
1994 |
if (abs(fl) < abs(fh)) then begin
|
1995 |
xl := xl+FACTOR*(xl-xh);
|
1996 |
fl := FDist(xl, DegreesFreedom1, DegreesFreedom2)-Probability;
|
1997 |
end else begin
|
1998 |
xh := xh+FACTOR*(xh-xl);
|
1999 |
fh := FDist(xh, DegreesFreedom1, DegreesFreedom2)-Probability;
|
2000 |
end;
|
2001 |
end;
|
2002 |
if (fl*fh >= 0.0) then
|
2003 |
{couldn't bracket it, means Probability too close to 0.0}
|
2004 |
RaiseStatError(stscStatNoConverge);
|
2005 |
|
2006 |
{Ridder's method of finding the root of FDist = Probability}
|
2007 |
ans := UNUSED;
|
2008 |
|
2009 |
for j := 1 to MAXIT do begin
|
2010 |
xm := 0.5*(xl+xh);
|
2011 |
fm := FDist(xm, DegreesFreedom1, DegreesFreedom2)-Probability;
|
2012 |
s := sqrt(fm*fm-fl*fh);
|
2013 |
if (s = 0.0) then begin
|
2014 |
Result := ans;
|
2015 |
exit;
|
2016 |
end;
|
2017 |
if (fl >= fh) then
|
2018 |
dsign := 1.0
|
2019 |
else
|
2020 |
dsign := -1.0;
|
2021 |
xnew := xm+(xm-xl)*(dsign*fm/s);
|
2022 |
if (abs(xnew-ans) <= XACC) then begin
|
2023 |
Result := ans;
|
2024 |
exit;
|
2025 |
end;
|
2026 |
ans := xnew;
|
2027 |
|
2028 |
fnew := FDist(ans, DegreesFreedom1, DegreesFreedom2)-Probability;
|
2029 |
if (fnew = 0.0) then begin
|
2030 |
Result := ans;
|
2031 |
exit;
|
2032 |
end;
|
2033 |
|
2034 |
{keep root bracketed on next iteration}
|
2035 |
if (Sign(fm, fnew) <> fm) then begin
|
2036 |
xl := xm;
|
2037 |
fl := fm;
|
2038 |
xh := ans;
|
2039 |
fh := fnew;
|
2040 |
end else if (Sign(fl, fnew) <> fl) then begin
|
2041 |
xh := ans;
|
2042 |
fh := fnew;
|
2043 |
end else if (Sign(fh, fnew) <> fh) then begin
|
2044 |
xl := ans;
|
2045 |
fl := fnew;
|
2046 |
end else
|
2047 |
{shouldn't get here}
|
2048 |
RaiseStatError(stscStatNoConverge);
|
2049 |
|
2050 |
if (abs(xh-xl) <= XACC) then begin
|
2051 |
Result := ans;
|
2052 |
exit;
|
2053 |
end;
|
2054 |
end;
|
2055 |
Result := 0.0; {avoid compiler warning}
|
2056 |
RaiseStatError(stscStatNoConverge);
|
2057 |
end;
|
2058 |
end;
|
2059 |
|
2060 |
function LogNormDist(X, Mean, StandardDev : Single) : Single;
|
2061 |
begin
|
2062 |
if (X <= 0.0) or (StandardDev <= 0) then
|
2063 |
RaiseStatError(stscStatBadParam);
|
2064 |
Result := NormSDist((ln(X)-Mean)/StandardDev);
|
2065 |
end;
|
2066 |
|
2067 |
function LogInv(Probability, Mean, StandardDev : Single) : Single;
|
2068 |
begin
|
2069 |
if (Probability < 0.0) or (Probability > 1.0) or (StandardDev <= 0) then
|
2070 |
RaiseStatError(stscStatBadParam);
|
2071 |
Result := exp(Mean+StandardDev*NormSInv(Probability));
|
2072 |
end;
|
2073 |
|
2074 |
function NormDist(X, Mean, StandardDev : Single;
|
2075 |
Cumulative : Boolean) : Single;
|
2076 |
var
|
2077 |
Z : Extended;
|
2078 |
begin
|
2079 |
if (StandardDev <= 0) then
|
2080 |
RaiseStatError(stscStatBadParam);
|
2081 |
Z := (X-Mean)/StandardDev;
|
2082 |
if (Cumulative) then
|
2083 |
Result := NormSDist(Z)
|
2084 |
else
|
2085 |
Result := exp(-Z*Z/2.0)/(StandardDev*sqrt2pi);
|
2086 |
end;
|
2087 |
|
2088 |
function NormInv(Probability, Mean, StandardDev : Single) : Single;
|
2089 |
begin
|
2090 |
if (Probability < 0.0) or (Probability > 1.0) or (StandardDev <= 0) then
|
2091 |
RaiseStatError(stscStatBadParam);
|
2092 |
Result := Mean+StandardDev*NormSInv(Probability);
|
2093 |
end;
|
2094 |
|
2095 |
function Erfc(X : Single) : Single;
|
2096 |
var
|
2097 |
t, z, ans : Double;
|
2098 |
begin
|
2099 |
z := abs(X);
|
2100 |
t := 1.0/(1.0+0.5*z);
|
2101 |
ans := t*exp(-z*z-1.26551223+t*(1.00002368+t*(0.37409196+t*(0.09678418+
|
2102 |
t*(-0.18628806+t*(0.27886807+t*(-1.13520398+t*(1.48851587+
|
2103 |
t*(-0.82215223+t*0.17087277)))))))));
|
2104 |
if (X >= 0.0) then
|
2105 |
Result := ans
|
2106 |
else
|
2107 |
Result := 2.0-ans;
|
2108 |
end;
|
2109 |
|
2110 |
function NormSDist(Z : Single) : Single;
|
2111 |
const
|
2112 |
sqrt2 = 1.41421356237310;
|
2113 |
begin
|
2114 |
Result := 1.0-0.5*Erfc(Z/sqrt2);
|
2115 |
end;
|
2116 |
|
2117 |
function NormSInv(Probability : Single) : Single;
|
2118 |
const
|
2119 |
MAXIT = 100;
|
2120 |
UNUSED = -1.11e30;
|
2121 |
XACC = 3e-7;
|
2122 |
FACTOR = 1.6;
|
2123 |
var
|
2124 |
j : Integer;
|
2125 |
ans, fh, fl, fm, fnew, s, xh, xl, xm, xnew, dsign : Double;
|
2126 |
begin
|
2127 |
if (Probability < 0.0) or (Probability > 1.0) then
|
2128 |
RaiseStatError(stscStatBadParam);
|
2129 |
Result := 0.0;
|
2130 |
|
2131 |
{bracket the interval}
|
2132 |
xl := -2.0;
|
2133 |
xh := +2.0;
|
2134 |
fl := NormSDist(xl)-Probability;
|
2135 |
fh := NormSDist(xh)-Probability;
|
2136 |
for j := 1 to MAXIT do begin
|
2137 |
if (fl*fh < 0.0) then
|
2138 |
{bracketed the root}
|
2139 |
break;
|
2140 |
if (abs(fl) < abs(fh)) then begin
|
2141 |
xl := xl+FACTOR*(xl-xh);
|
2142 |
fl := NormSDist(xl)-Probability;
|
2143 |
end else begin
|
2144 |
xh := xh+FACTOR*(xh-xl);
|
2145 |
fh := NormSDist(xh)-Probability;
|
2146 |
end;
|
2147 |
end;
|
2148 |
if (fl*fh >= 0.0) then
|
2149 |
{couldn't bracket it, means Probability too close to 0.0 or 1.0}
|
2150 |
RaiseStatError(stscStatNoConverge);
|
2151 |
|
2152 |
{Ridder's method of finding the root of NormSDist = Probability}
|
2153 |
ans := UNUSED;
|
2154 |
|
2155 |
for j := 1 to MAXIT do begin
|
2156 |
xm := 0.5*(xl+xh);
|
2157 |
fm := NormSDist(xm)-Probability;
|
2158 |
s := sqrt(fm*fm-fl*fh);
|
2159 |
if (s = 0.0) then begin
|
2160 |
Result := ans;
|
2161 |
exit;
|
2162 |
end;
|
2163 |
if (fl >= fh) then
|
2164 |
dsign := 1.0
|
2165 |
else
|
2166 |
dsign := -1.0;
|
2167 |
xnew := xm+(xm-xl)*(dsign*fm/s);
|
2168 |
if (abs(xnew-ans) <= XACC) then begin
|
2169 |
Result := ans;
|
2170 |
exit;
|
2171 |
end;
|
2172 |
ans := xnew;
|
2173 |
|
2174 |
fnew := NormSDist(ans)-Probability;
|
2175 |
if (fnew = 0.0) then begin
|
2176 |
Result := ans;
|
2177 |
exit;
|
2178 |
end;
|
2179 |
|
2180 |
{keep root bracketed on next iteration}
|
2181 |
if (Sign(fm, fnew) <> fm) then begin
|
2182 |
xl := xm;
|
2183 |
fl := fm;
|
2184 |
xh := ans;
|
2185 |
fh := fnew;
|
2186 |
end else if (Sign(fl, fnew) <> fl) then begin
|
2187 |
xh := ans;
|
2188 |
fh := fnew;
|
2189 |
end else if (Sign(fh, fnew) <> fh) then begin
|
2190 |
xl := ans;
|
2191 |
fl := fnew;
|
2192 |
end else
|
2193 |
{shouldn't get here}
|
2194 |
RaiseStatError(stscStatNoConverge);
|
2195 |
|
2196 |
if (abs(xh-xl) <= XACC) then begin
|
2197 |
Result := ans;
|
2198 |
exit;
|
2199 |
end;
|
2200 |
end;
|
2201 |
RaiseStatError(stscStatNoConverge);
|
2202 |
end;
|
2203 |
|
2204 |
function Poisson(X : Integer; Mean : Single; Cumulative : Boolean) : Single;
|
2205 |
begin
|
2206 |
if (X < 0) or (Mean <= 0.0) then
|
2207 |
RaiseStatError(stscStatBadParam);
|
2208 |
if (Cumulative) then
|
2209 |
Result := 1.0-GammP(X+1.0, Mean)
|
2210 |
else
|
2211 |
Result := IntPower(Mean, X)*exp(-Mean)/Factorial(X);
|
2212 |
end;
|
2213 |
|
2214 |
function TDist(X : Single; DegreesFreedom : Integer;
|
2215 |
TwoTails : Boolean) : Single;
|
2216 |
var
|
2217 |
a : Double;
|
2218 |
begin
|
2219 |
if (DegreesFreedom < 1) then
|
2220 |
RaiseStatError(stscStatBadParam);
|
2221 |
|
2222 |
a := BetaDist(DegreesFreedom/(DegreesFreedom+X*X), DegreesFreedom/2.0,
|
2223 |
0.5, 0.0, 1.0);
|
2224 |
if TwoTails then
|
2225 |
Result := a
|
2226 |
else
|
2227 |
Result := 0.5*a;
|
2228 |
end;
|
2229 |
|
2230 |
function TInv(Probability : Single; DegreesFreedom : Integer) : Single;
|
2231 |
const
|
2232 |
MAXIT = 100;
|
2233 |
UNUSED = -1.11e30;
|
2234 |
XACC = 3e-7;
|
2235 |
FACTOR = 1.6;
|
2236 |
var
|
2237 |
j : Integer;
|
2238 |
ans, fh, fl, fm, fnew, s, xh, xl, xm, xnew, dsign : Double;
|
2239 |
begin
|
2240 |
if (Probability < 0.0) or (Probability > 1.0) or (DegreesFreedom < 1) then
|
2241 |
RaiseStatError(stscStatBadParam);
|
2242 |
|
2243 |
Result := 0.0;
|
2244 |
if (Probability = 1.0) then
|
2245 |
exit;
|
2246 |
|
2247 |
{bracket the interval}
|
2248 |
xl := 0.0;
|
2249 |
xh := +2.0;
|
2250 |
fl := TDist(xl, DegreesFreedom, true)-Probability;
|
2251 |
fh := TDist(xh, DegreesFreedom, true)-Probability;
|
2252 |
for j := 1 to MAXIT do begin
|
2253 |
if (fl*fh < 0.0) then
|
2254 |
{bracketed the root}
|
2255 |
break;
|
2256 |
if (abs(fl) < abs(fh)) then begin
|
2257 |
xl := xl+FACTOR*(xl-xh);
|
2258 |
fl := TDist(xl, DegreesFreedom, true)-Probability;
|
2259 |
end else begin
|
2260 |
xh := xh+FACTOR*(xh-xl);
|
2261 |
fh := TDist(xh, DegreesFreedom, true)-Probability;
|
2262 |
end;
|
2263 |
end;
|
2264 |
if (fl*fh >= 0.0) then
|
2265 |
{couldn't bracket it, means Probability too close to 1.0}
|
2266 |
RaiseStatError(stscStatNoConverge);
|
2267 |
|
2268 |
{Ridder's method of finding the root of TDist = Probability}
|
2269 |
ans := UNUSED;
|
2270 |
|
2271 |
for j := 1 to MAXIT do begin
|
2272 |
xm := 0.5*(xl+xh);
|
2273 |
fm := TDist(xm, DegreesFreedom, true)-Probability;
|
2274 |
s := sqrt(fm*fm-fl*fh);
|
2275 |
if (s = 0.0) then begin
|
2276 |
Result := ans;
|
2277 |
exit;
|
2278 |
end;
|
2279 |
if (fl >= fh) then
|
2280 |
dsign := 1.0
|
2281 |
else
|
2282 |
dsign := -1.0;
|
2283 |
xnew := xm+(xm-xl)*(dsign*fm/s);
|
2284 |
if (abs(xnew-ans) <= XACC) then begin
|
2285 |
Result := ans;
|
2286 |
exit;
|
2287 |
end;
|
2288 |
ans := xnew;
|
2289 |
|
2290 |
fnew := TDist(ans, DegreesFreedom, true)-Probability;
|
2291 |
if (fnew = 0.0) then begin
|
2292 |
Result := ans;
|
2293 |
exit;
|
2294 |
end;
|
2295 |
|
2296 |
{keep root bracketed on next iteration}
|
2297 |
if (Sign(fm, fnew) <> fm) then begin
|
2298 |
xl := xm;
|
2299 |
fl := fm;
|
2300 |
xh := ans;
|
2301 |
fh := fnew;
|
2302 |
end else if (Sign(fl, fnew) <> fl) then begin
|
2303 |
xh := ans;
|
2304 |
fh := fnew;
|
2305 |
end else if (Sign(fh, fnew) <> fh) then begin
|
2306 |
xl := ans;
|
2307 |
fl := fnew;
|
2308 |
end else
|
2309 |
{shouldn't get here}
|
2310 |
RaiseStatError(stscStatNoConverge);
|
2311 |
|
2312 |
if (abs(xh-xl) <= XACC) then begin
|
2313 |
Result := ans;
|
2314 |
exit;
|
2315 |
end;
|
2316 |
end;
|
2317 |
RaiseStatError(stscStatNoConverge);
|
2318 |
end;
|
2319 |
|
2320 |
procedure Initialize;
|
2321 |
{-Fully initializes factorial lookup tables}
|
2322 |
var
|
2323 |
i : Integer;
|
2324 |
begin
|
2325 |
FactA[2] := 2.0;
|
2326 |
for i := 3 to MFactA do
|
2327 |
FactA[i] := i*FactA[i-1];
|
2328 |
for i := 2 to MFactLna do
|
2329 |
FactLnA[i] := GammaLn(i+1.0);
|
2330 |
end;
|
2331 |
|
2332 |
initialization
|
2333 |
Initialize;
|
2334 |
end.
|