diff docs/modules/txt/StatisticsUtil.txt @ 0:4816e4a8ae95 draft default tip

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+NAME
+    StatisticsUtil
+
+SYNOPSIS
+    use StatisticsUtil;
+
+    use Statistics qw(:all);
+
+DESCRIPTION
+    StatisticsUtil module provides the following functions:
+
+    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
+
+  METHODS
+    Average
+            $Value = Average(\@DataArray);
+
+        Computes the mean of an array of numbers: SUM( x[i] ) / n
+
+    AverageDeviation
+            $Value = AverageDeviation(\@DataArray);
+
+        Computes the average of the absolute deviation of an array of
+        numbers: SUM( ABS(x[i] - Xmean) ) / n
+
+    Correlation
+            $Value = Correlation(\@XDataArray, \@YDataArray);
+
+        Computes the Pearson correlation coefficient between two arrays of
+        numbers: SUM( (x[i] - Xmean)(y[i] - Ymean) ) / SQRT( SUM( (x[i] -
+        Xmean)^2 )(SUM( (y[i] - Ymean)^2 )) )
+
+    Euclidean
+            $Return = Euclidean(\@DataArray);
+
+        Computes the euclidean distance of an array of numbers: SQRT( SUM(
+        x[i] ** 2) )
+
+    Covariance
+            $Value = Covariance(\@XDataArray, \@YDataArray);
+
+        Computes the covariance between two arrays of numbers: SUM( (x[i] -
+        Xmean) (y[i] - Ymean) ) / n
+
+    Factorial
+            $Value = Factorial($Num);
+
+        Computes the factorial of a positive integer.
+
+    FactorialDivison
+            $Value = FactorialDivision($Numerator, $Denominator);
+
+        Compute the factorial divison of two positive integers.
+
+    Frequency
+            %FrequencyValues = Frequency(\@DataArray, [$NumOfBins]);
+            %FrequencyValues = Frequency(\@DataArray, [\@BinRange]);
+
+        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.
+
+    GeometricMean
+            $Value = GeometricMean(\@DataArray);
+
+        Computes the geometric mean of an array of numbers: NthROOT(
+        PRODUCT(x[i]) )
+
+    HarmonicMean
+            $Value = HarmonicMean(\@DataArray);
+
+        Computes the harmonic mean of an array of numbers: 1 / ( SUM(1/x[i])
+        / n )
+
+    KLargest
+            $Value = KLargest(\@DataArray, $KthNumber);
+
+        Returns the k-largest value from an array of numbers.
+
+    KSmallest
+            $Value = KSmallest(\@DataArray, $KthNumber);
+
+        Returns the k-smallest value from an array of numbers.
+
+    Kurtosis
+            $Value = Kurtosis(\@DataArray);
+
+        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)}
+
+    Maximum
+            $Value = Maximum(\@DataArray);
+
+        Returns the largest value from an array of numbers.
+
+    Minimum
+            $Value = Minimum(\@DataArray);
+
+        Returns the smallest value from an array of numbers.
+
+    Mean
+            $Value = Mean(\@DataArray);
+
+        Computes the mean of an array of numbers: SUM( x[i] ) / n
+
+    Median
+            $Value = Median(\@DataArray);
+
+        Computes the median value of an array of numbers. For an even number
+        array, it's the average of two middle values.
+
+        For even values of n: Xsorted[(n - 1)/2 + 1] For odd values of n:
+        (Xsorted[n/2] + Xsorted[n/2 + 1])/2
+
+    Mode
+            $Value = Mode(\@DataArray);
+
+        Returns the most frequently occuring value in an array of numbers.
+
+    PearsonCorrelation
+            $Value = Correlation(\@XDataArray, \@YDataArray);
+
+        Computes the Pearson correlation coefficient between two arrays of
+        numbers: SUM( (x[i] - Xmean)(y[i] - Ymean) ) / SQRT( SUM( (x[i] -
+        Xmean)^2 )(SUM( (y[i] - Ymean)^2 )) )
+
+    Permutations
+            $PermutationsRef = Permutations(@DataToPermute);
+
+        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.
+
+        This alogrithm is based on the example provided by Mark
+        Jason-Dominus, and is available at CPAN as mjd_permute standalone
+        script.
+
+    Product
+            $Value = Product(\@DataArray);
+
+        Compute the product of an array of numbers.
+
+    Range
+            ($Smallest, $Largest) = Range(\@DataArray);
+
+        Return the smallest and largest values from an array of numbers.
+
+    RSquare
+            $Value = RSquare(\@XDataArray, \@YDataArray);
+
+        Computes square of the Pearson correlation coefficient between two
+        arrays of numbers.
+
+    Skewness
+            $Value = Skewness(\@DataArray);
+
+        Computes the skewness of an array of numbers: {n/(n - 1)(n - 2)}
+        SUM{ ((x[i] - Xmean)/STDDEV)^3 }
+
+    StandardDeviation
+            $Value = StandardDeviation(\@DataArray);
+
+        Computes the standard deviation of an array of numbers. SQRT ( SUM(
+        (x[i] - mean)^2 ) / (n - 1) )
+
+    StandardDeviationN
+            $Value = StandardDeviationN(\@DataArray);
+
+        Computes the standard deviation of an array of numbers representing
+        entire population: SQRT ( SUM( (x[i] - mean)^2 ) / n )
+
+    StandardError
+            $Value = StandardError($StandardDeviation, $Count);
+
+        Computes the standard error using standard deviation and sample
+        size.
+
+    Standardize
+            $Value = Standardize($Value, $Mean, $StandardDeviation);
+
+        Standardizes the value using mean and standard deviation.
+
+    StandardScores
+            @Values = StandardScores(\@DataArray);
+
+        Computes the standard deviation above the mean for an array of
+        numbers: (x[i] - mean) / (n - 1)
+
+    StandardScoresN
+            @Values = StandardScoresN(\@DataArray);
+
+        Computes the standard deviation above the mean for an array of
+        numbers representing entire population: (x[i] - mean) / n
+
+    Sum
+            $Value = Sum(\@DataArray);
+
+        Compute the sum of an array of numbers.
+
+    SumOfSquares
+            $Value = SumOfSquares(\@DataArray);
+
+        Computes the sum of an array of numbers.
+
+    TrimMean
+            $Value = TrimMean(\@DataArray, $FractionToExclude));
+
+        Computes the mean of an array of numbers by excluding a fraction of
+        numbers from the top and bottom of the data set.
+
+    Variance
+            $Value = Variance(\@DataArray);
+
+        Computes the variance of an array of numbers: SUM( (x[i] - Xmean)^2
+        / (n - 1) )
+
+    VarianceN
+            $Value = Variance(\@DataArray);
+
+        Compute the variance of an array of numbers representing entire
+        population: SUM( (x[i] - Xmean)^2 / n )
+
+AUTHOR
+    Manish Sud <[e-mail]>
+
+SEE ALSO
+    Constants.pm, ConversionsUtil.pm, MathUtil.pm
+
+COPYRIGHT
+    Copyright (C) 2015 Manish Sud. All rights reserved.
+
+    This file is part of MayaChemTools.
+
+    MayaChemTools is free software; you can redistribute it and/or modify it
+    under the terms of the GNU Lesser General Public License as published by
+    the Free Software Foundation; either version 3 of the License, or (at
+    your option) any later version.
+