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| author | deepakjadmin |
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| date | Wed, 20 Jan 2016 11:55:01 -0500 |
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--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/mayachemtools/docs/modules/man3/StatisticsUtil.3 Wed Jan 20 11:55:01 2016 -0500 @@ -0,0 +1,434 @@ +.\" Automatically generated by Pod::Man 2.25 (Pod::Simple 3.22) +.\" +.\" Standard preamble: +.\" ======================================================================== +.de Sp \" Vertical space (when we can't use .PP) +.if t .sp .5v +.if n .sp +.. +.de Vb \" Begin verbatim text +.ft CW +.nf +.ne \\$1 +.. +.de Ve \" End verbatim text +.ft R +.fi +.. +.\" Set up some character translations and predefined strings. \*(-- will +.\" give an unbreakable dash, \*(PI will give pi, \*(L" will give a left +.\" double quote, and \*(R" will give a right double quote. \*(C+ will +.\" give a nicer C++. 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Always turn off hyphenation; it makes +.\" way too many mistakes in technical documents. +.if n .ad l +.nh +.SH "NAME" +StatisticsUtil +.SH "SYNOPSIS" +.IX Header "SYNOPSIS" +use StatisticsUtil; +.PP +use Statistics qw(:all); +.SH "DESCRIPTION" +.IX Header "DESCRIPTION" +\&\fBStatisticsUtil\fR module provides the following functions: +.PP +Average, AverageDeviation, Correlation, Covariance, Euclidean, Factorial, +FactorialDivison, Frequency, GeometricMean, HarmonicMean, KLargest, KSmallest, +Kurtosis, Maximum, Mean, Median, Minimum, Mode, PearsonCorrelation, Permutations, +Product, RSquare, Range, Skewness, StandardDeviation, StandardDeviationN, +StandardError, StandardScores, StandardScoresN, Standardize, Sum, SumOfSquares, +TrimMean, Variance, VarianceN +.SS "\s-1METHODS\s0" +.IX Subsection "METHODS" +.IP "\fBAverage\fR" 4 +.IX Item "Average" +.Vb 1 +\& $Value = Average(\e@DataArray); +.Ve +.Sp +Computes the mean of an array of numbers: \s-1SUM\s0( x[i] ) / n +.IP "\fBAverageDeviation\fR" 4 +.IX Item "AverageDeviation" +.Vb 1 +\& $Value = AverageDeviation(\e@DataArray); +.Ve +.Sp +Computes the average of the absolute deviation of an array of numbers: \s-1SUM\s0( \s-1ABS\s0(x[i] \- Xmean) ) / n +.IP "\fBCorrelation\fR" 4 +.IX Item "Correlation" +.Vb 1 +\& $Value = Correlation(\e@XDataArray, \e@YDataArray); +.Ve +.Sp +Computes the Pearson correlation coefficient between two arrays of numbers: +\&\s-1SUM\s0( (x[i] \- Xmean)(y[i] \- Ymean) ) / \s-1SQRT\s0( \s-1SUM\s0( (x[i] \- Xmean)^2 )(\s-1SUM\s0( (y[i] \- Ymean)^2 )) ) +.IP "\fBEuclidean\fR" 4 +.IX Item "Euclidean" +.Vb 1 +\& $Return = Euclidean(\e@DataArray); +.Ve +.Sp +Computes the euclidean distance of an array of numbers: \s-1SQRT\s0( \s-1SUM\s0( x[i] ** 2) ) +.IP "\fBCovariance\fR" 4 +.IX Item "Covariance" +.Vb 1 +\& $Value = Covariance(\e@XDataArray, \e@YDataArray); +.Ve +.Sp +Computes the covariance between two arrays of numbers: \s-1SUM\s0( (x[i] \- Xmean) (y[i] \- Ymean) ) / n +.IP "\fBFactorial\fR" 4 +.IX Item "Factorial" +.Vb 1 +\& $Value = Factorial($Num); +.Ve +.Sp +Computes the factorial of a positive integer. +.IP "\fBFactorialDivison\fR" 4 +.IX Item "FactorialDivison" +.Vb 1 +\& $Value = FactorialDivision($Numerator, $Denominator); +.Ve +.Sp +Compute the factorial divison of two positive integers. +.IP "\fBFrequency\fR" 4 +.IX Item "Frequency" +.Vb 2 +\& %FrequencyValues = Frequency(\e@DataArray, [$NumOfBins]); +\& %FrequencyValues = Frequency(\e@DataArray, [\e@BinRange]); +.Ve +.Sp +A hash array is returned with keys and values representing range and frequency values, respectively. +The frequency value for a specific key corresponds to all the values which are greater than +the previous key and less than or equal to the current key. A key value representing maximum value is +added for generating frequency distribution for specific number of bins, and whenever the maximum +array value is greater than the maximum specified in bin range, it is also added to bin range. +.IP "\fBGeometricMean\fR" 4 +.IX Item "GeometricMean" +.Vb 1 +\& $Value = GeometricMean(\e@DataArray); +.Ve +.Sp +Computes the geometric mean of an array of numbers: NthROOT( \s-1PRODUCT\s0(x[i]) ) +.IP "\fBHarmonicMean\fR" 4 +.IX Item "HarmonicMean" +.Vb 1 +\& $Value = HarmonicMean(\e@DataArray); +.Ve +.Sp +Computes the harmonic mean of an array of numbers: 1 / ( \s-1SUM\s0(1/x[i]) / n ) +.IP "\fBKLargest\fR" 4 +.IX Item "KLargest" +.Vb 1 +\& $Value = KLargest(\e@DataArray, $KthNumber); +.Ve +.Sp +Returns the k\-largest value from an array of numbers. +.IP "\fBKSmallest\fR" 4 +.IX Item "KSmallest" +.Vb 1 +\& $Value = KSmallest(\e@DataArray, $KthNumber); +.Ve +.Sp +Returns the k\-smallest value from an array of numbers. +.IP "\fBKurtosis\fR" 4 +.IX Item "Kurtosis" +.Vb 1 +\& $Value = Kurtosis(\e@DataArray); +.Ve +.Sp +Computes the kurtosis of an array of numbers: +[ {n(n + 1)/(n \- 1)(n \- 2)(n \- 3)} SUM{ ((x[i] \- Xmean)/STDDEV)^4 } ] \- {3((n \- 1)^2)}/{(n \- 2)(n\-3)} +.IP "\fBMaximum\fR" 4 +.IX Item "Maximum" +.Vb 1 +\& $Value = Maximum(\e@DataArray); +.Ve +.Sp +Returns the largest value from an array of numbers. +.IP "\fBMinimum\fR" 4 +.IX Item "Minimum" +.Vb 1 +\& $Value = Minimum(\e@DataArray); +.Ve +.Sp +Returns the smallest value from an array of numbers. +.IP "\fBMean\fR" 4 +.IX Item "Mean" +.Vb 1 +\& $Value = Mean(\e@DataArray); +.Ve +.Sp +Computes the mean of an array of numbers: \s-1SUM\s0( x[i] ) / n +.IP "\fBMedian\fR" 4 +.IX Item "Median" +.Vb 1 +\& $Value = Median(\e@DataArray); +.Ve +.Sp +Computes the median value of an array of numbers. For an even number array, it's +the average of two middle values. +.Sp +For even values of n: Xsorted[(n \- 1)/2 + 1] +For odd values of n: (Xsorted[n/2] + Xsorted[n/2 + 1])/2 +.IP "\fBMode\fR" 4 +.IX Item "Mode" +.Vb 1 +\& $Value = Mode(\e@DataArray); +.Ve +.Sp +Returns the most frequently occuring value in an array of numbers. +.IP "\fBPearsonCorrelation\fR" 4 +.IX Item "PearsonCorrelation" +.Vb 1 +\& $Value = Correlation(\e@XDataArray, \e@YDataArray); +.Ve +.Sp +Computes the Pearson correlation coefficient between two arrays of numbers: +\&\s-1SUM\s0( (x[i] \- Xmean)(y[i] \- Ymean) ) / \s-1SQRT\s0( \s-1SUM\s0( (x[i] \- Xmean)^2 )(\s-1SUM\s0( (y[i] \- Ymean)^2 )) ) +.IP "\fBPermutations\fR" 4 +.IX Item "Permutations" +.Vb 1 +\& $PermutationsRef = Permutations(@DataToPermute); +.Ve +.Sp +Generate all possible permuations or a specific permutations of items in an array +and return a reference to an array containing array references to generated permuations. +.Sp +This alogrithm is based on the example provided by Mark Jason-Dominus, and is available +at \s-1CPAN\s0 as mjd_permute standalone script. +.IP "\fBProduct\fR" 4 +.IX Item "Product" +.Vb 1 +\& $Value = Product(\e@DataArray); +.Ve +.Sp +Compute the product of an array of numbers. +.IP "\fBRange\fR" 4 +.IX Item "Range" +.Vb 1 +\& ($Smallest, $Largest) = Range(\e@DataArray); +.Ve +.Sp +Return the smallest and largest values from an array of numbers. +.IP "\fBRSquare\fR" 4 +.IX Item "RSquare" +.Vb 1 +\& $Value = RSquare(\e@XDataArray, \e@YDataArray); +.Ve +.Sp +Computes square of the Pearson correlation coefficient between two arrays of numbers. +.IP "\fBSkewness\fR" 4 +.IX Item "Skewness" +.Vb 1 +\& $Value = Skewness(\e@DataArray); +.Ve +.Sp +Computes the skewness of an array of numbers: +{n/(n \- 1)(n \- 2)} SUM{ ((x[i] \- Xmean)/STDDEV)^3 } +.IP "\fBStandardDeviation\fR" 4 +.IX Item "StandardDeviation" +.Vb 1 +\& $Value = StandardDeviation(\e@DataArray); +.Ve +.Sp +Computes the standard deviation of an array of numbers. +\&\s-1SQRT\s0 ( \s-1SUM\s0( (x[i] \- mean)^2 ) / (n \- 1) ) +.IP "\fBStandardDeviationN\fR" 4 +.IX Item "StandardDeviationN" +.Vb 1 +\& $Value = StandardDeviationN(\e@DataArray); +.Ve +.Sp +Computes the standard deviation of an array of numbers representing entire population: +\&\s-1SQRT\s0 ( \s-1SUM\s0( (x[i] \- mean)^2 ) / n ) +.IP "\fBStandardError\fR" 4 +.IX Item "StandardError" +.Vb 1 +\& $Value = StandardError($StandardDeviation, $Count); +.Ve +.Sp +Computes the standard error using standard deviation and sample size. +.IP "\fBStandardize\fR" 4 +.IX Item "Standardize" +.Vb 1 +\& $Value = Standardize($Value, $Mean, $StandardDeviation); +.Ve +.Sp +Standardizes the value using mean and standard deviation. +.IP "\fBStandardScores\fR" 4 +.IX Item "StandardScores" +.Vb 1 +\& @Values = StandardScores(\e@DataArray); +.Ve +.Sp +Computes the standard deviation above the mean for an array of numbers: +(x[i] \- mean) / (n \- 1) +.IP "\fBStandardScoresN\fR" 4 +.IX Item "StandardScoresN" +.Vb 1 +\& @Values = StandardScoresN(\e@DataArray); +.Ve +.Sp +Computes the standard deviation above the mean for an array of numbers representing entire population: +(x[i] \- mean) / n +.IP "\fBSum\fR" 4 +.IX Item "Sum" +.Vb 1 +\& $Value = Sum(\e@DataArray); +.Ve +.Sp +Compute the sum of an array of numbers. +.IP "\fBSumOfSquares\fR" 4 +.IX Item "SumOfSquares" +.Vb 1 +\& $Value = SumOfSquares(\e@DataArray); +.Ve +.Sp +Computes the sum of an array of numbers. +.IP "\fBTrimMean\fR" 4 +.IX Item "TrimMean" +.Vb 1 +\& $Value = TrimMean(\e@DataArray, $FractionToExclude)); +.Ve +.Sp +Computes the mean of an array of numbers by excluding a fraction of +numbers from the top and bottom of the data set. +.IP "\fBVariance\fR" 4 +.IX Item "Variance" +.Vb 1 +\& $Value = Variance(\e@DataArray); +.Ve +.Sp +Computes the variance of an array of numbers: \s-1SUM\s0( (x[i] \- Xmean)^2 / (n \- 1) ) +.IP "\fBVarianceN\fR" 4 +.IX Item "VarianceN" +.Vb 1 +\& $Value = Variance(\e@DataArray); +.Ve +.Sp +Compute the variance of an array of numbers representing entire population: +\&\s-1SUM\s0( (x[i] \- Xmean)^2 / n ) +.SH "AUTHOR" +.IX Header "AUTHOR" +Manish Sud <msud@san.rr.com> +.SH "SEE ALSO" +.IX Header "SEE ALSO" +Constants.pm, ConversionsUtil.pm, MathUtil.pm +.SH "COPYRIGHT" +.IX Header "COPYRIGHT" +Copyright (C) 2015 Manish Sud. All rights reserved. +.PP +This file is part of MayaChemTools. +.PP +MayaChemTools is free software; you can redistribute it and/or modify it under +the terms of the \s-1GNU\s0 Lesser General Public License as published by the Free +Software Foundation; either version 3 of the License, or (at your option) +any later version.