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3 <title>MayaChemTools:Documentation:StatisticsUtil.pm</title>
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14 <table width="100%" border=0 cellpadding=0 cellspacing=2>
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15 <tr align="left" valign="top"><td width="33%" align="left"><a href="./SequenceFileUtil.html" title="SequenceFileUtil.html">Previous</a> <a href="./index.html" title="Table of Contents">TOC</a> <a href="./TextUtil.html" title="TextUtil.html">Next</a></td><td width="34%" align="middle"><strong>StatisticsUtil.pm</strong></td><td width="33%" align="right"><a href="././code/StatisticsUtil.html" title="View source code">Code</a> | <a href="./../pdf/StatisticsUtil.pdf" title="PDF US Letter Size">PDF</a> | <a href="./../pdfgreen/StatisticsUtil.pdf" title="PDF US Letter Size with narrow margins: www.changethemargins.com">PDFGreen</a> | <a href="./../pdfa4/StatisticsUtil.pdf" title="PDF A4 Size">PDFA4</a> | <a href="./../pdfa4green/StatisticsUtil.pdf" title="PDF A4 Size with narrow margins: www.changethemargins.com">PDFA4Green</a></td></tr>
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16 </table>
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17 </div>
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18 <p>
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19 </p>
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20 <h2>NAME</h2>
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21 <p>StatisticsUtil</p>
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22 <p>
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23 </p>
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24 <h2>SYNOPSIS</h2>
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25 <p>use StatisticsUtil;</p>
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26 <p>use Statistics qw(:all);</p>
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27 <p>
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28 </p>
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29 <h2>DESCRIPTION</h2>
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30 <p><strong>StatisticsUtil</strong> module provides the following functions:</p>
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31 <p> <a href="#average">Average</a>, <a href="#averagedeviation">AverageDeviation</a>, <a href="#correlation">Correlation</a>, <a href="#covariance">Covariance</a>, <a href="#euclidean">Euclidean</a>, <a href="#factorial">Factorial</a>
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32 , <a href="#factorialdivison">FactorialDivison</a>, <a href="#frequency">Frequency</a>, <a href="#geometricmean">GeometricMean</a>, <a href="#harmonicmean">HarmonicMean</a>, <a href="#klargest">KLargest</a>, <a href="#ksmallest">KSmallest</a>
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33 , <a href="#kurtosis">Kurtosis</a>, <a href="#maximum">Maximum</a>, <a href="#mean">Mean</a>, <a href="#median">Median</a>, <a href="#minimum">Minimum</a>, <a href="#mode">Mode</a>, <a href="#pearsoncorrelation">PearsonCorrelation</a>, <a href="#permutations">Permutations</a>
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34 , <a href="#product">Product</a>, <a href="#rsquare">RSquare</a>, <a href="#range">Range</a>, <a href="#skewness">Skewness</a>, <a href="#standarddeviation">StandardDeviation</a>, <a href="#standarddeviationn">StandardDeviationN</a>
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35 , <a href="#standarderror">StandardError</a>, <a href="#standardscores">StandardScores</a>, <a href="#standardscoresn">StandardScoresN</a>, <a href="#standardize">Standardize</a>, <a href="#sum">Sum</a>, <a href="#sumofsquares">SumOfSquares</a>
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36 , <a href="#trimmean">TrimMean</a>, <a href="#variance">Variance</a>, <a href="#variancen">VarianceN</a>
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37 </p><p>
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38 </p>
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39 <h2>METHODS</h2>
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40 <dl>
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41 <dt><strong><a name="average" class="item"><strong>Average</strong></a></strong></dt>
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42 <dd>
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43 <div class="OptionsBox">
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44 $Value = Average(\@DataArray);</div>
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45 <p>Computes the mean of an array of numbers: SUM( x[i] ) / n</p>
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46 </dd>
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47 <dt><strong><a name="averagedeviation" class="item"><strong>AverageDeviation</strong></a></strong></dt>
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48 <dd>
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49 <div class="OptionsBox">
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50 $Value = AverageDeviation(\@DataArray);</div>
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51 <p>Computes the average of the absolute deviation of an array of numbers: SUM( ABS(x[i] - Xmean) ) / n</p>
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52 </dd>
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53 <dt><strong><a name="correlation" class="item"><strong>Correlation</strong></a></strong></dt>
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54 <dd>
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55 <div class="OptionsBox">
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56 $Value = Correlation(\@XDataArray, \@YDataArray);</div>
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57 <p>Computes the Pearson correlation coefficient between two arrays of numbers:
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58 SUM( (x[i] - Xmean)(y[i] - Ymean) ) / SQRT( SUM( (x[i] - Xmean)^2 )(SUM( (y[i] - Ymean)^2 )) )</p>
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59 </dd>
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60 <dt><strong><a name="euclidean" class="item"><strong>Euclidean</strong></a></strong></dt>
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61 <dd>
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62 <div class="OptionsBox">
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63 $Return = Euclidean(\@DataArray);</div>
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64 <p>Computes the euclidean distance of an array of numbers: SQRT( SUM( x[i] ** 2) )</p>
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65 </dd>
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66 <dt><strong><a name="covariance" class="item"><strong>Covariance</strong></a></strong></dt>
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67 <dd>
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68 <div class="OptionsBox">
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69 $Value = Covariance(\@XDataArray, \@YDataArray);</div>
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70 <p>Computes the covariance between two arrays of numbers: SUM( (x[i] - Xmean) (y[i] - Ymean) ) / n</p>
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71 </dd>
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72 <dt><strong><a name="factorial" class="item"><strong>Factorial</strong></a></strong></dt>
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73 <dd>
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74 <div class="OptionsBox">
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75 $Value = Factorial($Num);</div>
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76 <p>Computes the factorial of a positive integer.</p>
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77 </dd>
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78 <dt><strong><a name="factorialdivison" class="item"><strong>FactorialDivison</strong></a></strong></dt>
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79 <dd>
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80 <div class="OptionsBox">
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81 $Value = FactorialDivision($Numerator, $Denominator);</div>
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82 <p>Compute the factorial divison of two positive integers.</p>
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83 </dd>
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84 <dt><strong><a name="frequency" class="item"><strong>Frequency</strong></a></strong></dt>
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85 <dd>
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86 <div class="OptionsBox">
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87 %FrequencyValues = Frequency(\@DataArray, [$NumOfBins]);
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88 <br/> %FrequencyValues = Frequency(\@DataArray, [\@BinRange]);</div>
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89 <p>A hash array is returned with keys and values representing range and frequency values, respectively.
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90 The frequency value for a specific key corresponds to all the values which are greater than
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91 the previous key and less than or equal to the current key. A key value representing maximum value is
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92 added for generating frequency distribution for specific number of bins, and whenever the maximum
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93 array value is greater than the maximum specified in bin range, it is also added to bin range.</p>
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94 </dd>
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95 <dt><strong><a name="geometricmean" class="item"><strong>GeometricMean</strong></a></strong></dt>
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96 <dd>
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97 <div class="OptionsBox">
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98 $Value = GeometricMean(\@DataArray);</div>
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99 <p>Computes the geometric mean of an array of numbers: NthROOT( PRODUCT(x[i]) )</p>
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100 </dd>
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101 <dt><strong><a name="harmonicmean" class="item"><strong>HarmonicMean</strong></a></strong></dt>
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102 <dd>
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103 <div class="OptionsBox">
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104 $Value = HarmonicMean(\@DataArray);</div>
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105 <p>Computes the harmonic mean of an array of numbers: 1 / ( SUM(1/x[i]) / n )</p>
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106 </dd>
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107 <dt><strong><a name="klargest" class="item"><strong>KLargest</strong></a></strong></dt>
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108 <dd>
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109 <div class="OptionsBox">
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110 $Value = KLargest(\@DataArray, $KthNumber);</div>
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111 <p>Returns the k-largest value from an array of numbers.</p>
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112 </dd>
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113 <dt><strong><a name="ksmallest" class="item"><strong>KSmallest</strong></a></strong></dt>
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114 <dd>
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115 <div class="OptionsBox">
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116 $Value = KSmallest(\@DataArray, $KthNumber);</div>
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117 <p>Returns the k-smallest value from an array of numbers.</p>
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118 </dd>
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119 <dt><strong><a name="kurtosis" class="item"><strong>Kurtosis</strong></a></strong></dt>
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120 <dd>
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121 <div class="OptionsBox">
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122 $Value = Kurtosis(\@DataArray);</div>
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123 <p>Computes the kurtosis of an array of numbers:
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124 [ {n(n + 1)/(n - 1)(n - 2)(n - 3)} SUM{ ((x[i] - Xmean)/STDDEV)^4 } ] - {3((n - 1)^2)}/{(n - 2)(n-3)}</p>
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125 </dd>
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126 <dt><strong><a name="maximum" class="item"><strong>Maximum</strong></a></strong></dt>
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127 <dd>
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128 <div class="OptionsBox">
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129 $Value = Maximum(\@DataArray);</div>
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130 <p>Returns the largest value from an array of numbers.</p>
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131 </dd>
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132 <dt><strong><a name="minimum" class="item"><strong>Minimum</strong></a></strong></dt>
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133 <dd>
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134 <div class="OptionsBox">
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135 $Value = Minimum(\@DataArray);</div>
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136 <p>Returns the smallest value from an array of numbers.</p>
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137 </dd>
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138 <dt><strong><a name="mean" class="item"><strong>Mean</strong></a></strong></dt>
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139 <dd>
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140 <div class="OptionsBox">
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141 $Value = Mean(\@DataArray);</div>
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142 <p>Computes the mean of an array of numbers: SUM( x[i] ) / n</p>
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143 </dd>
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144 <dt><strong><a name="median" class="item"><strong>Median</strong></a></strong></dt>
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145 <dd>
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146 <div class="OptionsBox">
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147 $Value = Median(\@DataArray);</div>
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148 <p>Computes the median value of an array of numbers. For an even number array, it's
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149 the average of two middle values.</p>
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150 <p>For even values of n: Xsorted[(n - 1)/2 + 1]
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151 For odd values of n: (Xsorted[n/2] + Xsorted[n/2 + 1])/2</p>
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152 </dd>
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153 <dt><strong><a name="mode" class="item"><strong>Mode</strong></a></strong></dt>
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154 <dd>
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155 <div class="OptionsBox">
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156 $Value = Mode(\@DataArray);</div>
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157 <p>Returns the most frequently occuring value in an array of numbers.</p>
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158 </dd>
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159 <dt><strong><a name="pearsoncorrelation" class="item"><strong>PearsonCorrelation</strong></a></strong></dt>
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160 <dd>
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161 <div class="OptionsBox">
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162 $Value = Correlation(\@XDataArray, \@YDataArray);</div>
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163 <p>Computes the Pearson correlation coefficient between two arrays of numbers:
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164 SUM( (x[i] - Xmean)(y[i] - Ymean) ) / SQRT( SUM( (x[i] - Xmean)^2 )(SUM( (y[i] - Ymean)^2 )) )</p>
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165 </dd>
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166 <dt><strong><a name="permutations" class="item"><strong>Permutations</strong></a></strong></dt>
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167 <dd>
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168 <div class="OptionsBox">
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169 $PermutationsRef = Permutations(@DataToPermute);</div>
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170 <p>Generate all possible permuations or a specific permutations of items in an array
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171 and return a reference to an array containing array references to generated permuations.</p>
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172 <p>This alogrithm is based on the example provided by Mark Jason-Dominus, and is available
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173 at CPAN as mjd_permute standalone script.</p>
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174 </dd>
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175 <dt><strong><a name="product" class="item"><strong>Product</strong></a></strong></dt>
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176 <dd>
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177 <div class="OptionsBox">
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178 $Value = Product(\@DataArray);</div>
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179 <p>Compute the product of an array of numbers.</p>
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180 </dd>
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181 <dt><strong><a name="range" class="item"><strong>Range</strong></a></strong></dt>
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182 <dd>
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183 <div class="OptionsBox">
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184 ($Smallest, $Largest) = Range(\@DataArray);</div>
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185 <p>Return the smallest and largest values from an array of numbers.</p>
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186 </dd>
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187 <dt><strong><a name="rsquare" class="item"><strong>RSquare</strong></a></strong></dt>
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188 <dd>
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189 <div class="OptionsBox">
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190 $Value = RSquare(\@XDataArray, \@YDataArray);</div>
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191 <p>Computes square of the Pearson correlation coefficient between two arrays of numbers.</p>
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192 </dd>
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193 <dt><strong><a name="skewness" class="item"><strong>Skewness</strong></a></strong></dt>
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194 <dd>
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195 <div class="OptionsBox">
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196 $Value = Skewness(\@DataArray);</div>
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197 <p>Computes the skewness of an array of numbers:
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198 {n/(n - 1)(n - 2)} SUM{ ((x[i] - Xmean)/STDDEV)^3 }</p>
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199 </dd>
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200 <dt><strong><a name="standarddeviation" class="item"><strong>StandardDeviation</strong></a></strong></dt>
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201 <dd>
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202 <div class="OptionsBox">
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203 $Value = StandardDeviation(\@DataArray);</div>
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204 <p>Computes the standard deviation of an array of numbers.
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205 SQRT ( SUM( (x[i] - mean)^2 ) / (n - 1) )</p>
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206 </dd>
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207 <dt><strong><a name="standarddeviationn" class="item"><strong>StandardDeviationN</strong></a></strong></dt>
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208 <dd>
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209 <div class="OptionsBox">
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210 $Value = StandardDeviationN(\@DataArray);</div>
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211 <p>Computes the standard deviation of an array of numbers representing entire population:
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212 SQRT ( SUM( (x[i] - mean)^2 ) / n )</p>
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213 </dd>
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214 <dt><strong><a name="standarderror" class="item"><strong>StandardError</strong></a></strong></dt>
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215 <dd>
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216 <div class="OptionsBox">
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217 $Value = StandardError($StandardDeviation, $Count);</div>
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218 <p>Computes the standard error using standard deviation and sample size.</p>
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219 </dd>
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220 <dt><strong><a name="standardize" class="item"><strong>Standardize</strong></a></strong></dt>
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221 <dd>
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222 <div class="OptionsBox">
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223 $Value = Standardize($Value, $Mean, $StandardDeviation);</div>
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224 <p>Standardizes the value using mean and standard deviation.</p>
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225 </dd>
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226 <dt><strong><a name="standardscores" class="item"><strong>StandardScores</strong></a></strong></dt>
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227 <dd>
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228 <div class="OptionsBox">
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229 @Values = StandardScores(\@DataArray);</div>
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230 <p>Computes the standard deviation above the mean for an array of numbers:
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231 (x[i] - mean) / (n - 1)</p>
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232 </dd>
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233 <dt><strong><a name="standardscoresn" class="item"><strong>StandardScoresN</strong></a></strong></dt>
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234 <dd>
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235 <div class="OptionsBox">
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236 @Values = StandardScoresN(\@DataArray);</div>
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237 <p>Computes the standard deviation above the mean for an array of numbers representing entire population:
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238 (x[i] - mean) / n</p>
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239 </dd>
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240 <dt><strong><a name="sum" class="item"><strong>Sum</strong></a></strong></dt>
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241 <dd>
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242 <div class="OptionsBox">
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243 $Value = Sum(\@DataArray);</div>
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244 <p>Compute the sum of an array of numbers.</p>
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245 </dd>
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246 <dt><strong><a name="sumofsquares" class="item"><strong>SumOfSquares</strong></a></strong></dt>
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247 <dd>
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248 <div class="OptionsBox">
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249 $Value = SumOfSquares(\@DataArray);</div>
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250 <p>Computes the sum of an array of numbers.</p>
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251 </dd>
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252 <dt><strong><a name="trimmean" class="item"><strong>TrimMean</strong></a></strong></dt>
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253 <dd>
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254 <div class="OptionsBox">
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255 $Value = TrimMean(\@DataArray, $FractionToExclude));</div>
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256 <p>Computes the mean of an array of numbers by excluding a fraction of
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257 numbers from the top and bottom of the data set.</p>
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258 </dd>
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259 <dt><strong><a name="variance" class="item"><strong>Variance</strong></a></strong></dt>
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260 <dd>
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261 <div class="OptionsBox">
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262 $Value = Variance(\@DataArray);</div>
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263 <p>Computes the variance of an array of numbers: SUM( (x[i] - Xmean)^2 / (n - 1) )</p>
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264 </dd>
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265 <dt><strong><a name="variancen" class="item"><strong>VarianceN</strong></a></strong></dt>
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266 <dd>
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267 <div class="OptionsBox">
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268 $Value = Variance(\@DataArray);</div>
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269 <p>Compute the variance of an array of numbers representing entire population:
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270 SUM( (x[i] - Xmean)^2 / n )</p>
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271 </dd>
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272 </dl>
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273 <p>
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274 </p>
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275 <h2>AUTHOR</h2>
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276 <p><a href="mailto:msud@san.rr.com">Manish Sud</a></p>
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277 <p>
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278 </p>
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279 <h2>SEE ALSO</h2>
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280 <p><a href="./Constants.html">Constants.pm</a>, <a href="./ConversionsUtil.html">ConversionsUtil.pm</a>, <a href="./MathUtil.html">MathUtil.pm</a>
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281 </p>
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282 <p>
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283 </p>
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284 <h2>COPYRIGHT</h2>
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285 <p>Copyright (C) 2015 Manish Sud. All rights reserved.</p>
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286 <p>This file is part of MayaChemTools.</p>
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287 <p>MayaChemTools is free software; you can redistribute it and/or modify it under
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288 the terms of the GNU Lesser General Public License as published by the Free
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289 Software Foundation; either version 3 of the License, or (at your option)
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290 any later version.</p>
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291 <p> </p><p> </p><div class="DocNav">
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292 <table width="100%" border=0 cellpadding=0 cellspacing=2>
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293 <tr align="left" valign="top"><td width="33%" align="left"><a href="./SequenceFileUtil.html" title="SequenceFileUtil.html">Previous</a> <a href="./index.html" title="Table of Contents">TOC</a> <a href="./TextUtil.html" title="TextUtil.html">Next</a></td><td width="34%" align="middle"><strong>March 29, 2015</strong></td><td width="33%" align="right"><strong>StatisticsUtil.pm</strong></td></tr>
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294 </table>
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295 </div>
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296 <br />
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297 <center>
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298 <img src="../../images/h2o2.png">
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299 </center>
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300 </body>
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301 </html>
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