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1 NAME
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2 StatisticsUtil
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3
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4 SYNOPSIS
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5 use StatisticsUtil;
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6
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7 use Statistics qw(:all);
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8
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9 DESCRIPTION
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10 StatisticsUtil module provides the following functions:
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11
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12 Average, AverageDeviation, Correlation, Covariance, Euclidean,
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13 Factorial, FactorialDivison, Frequency, GeometricMean, HarmonicMean,
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14 KLargest, KSmallest, Kurtosis, Maximum, Mean, Median, Minimum, Mode,
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15 PearsonCorrelation, Permutations, Product, RSquare, Range, Skewness,
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16 StandardDeviation, StandardDeviationN, StandardError, StandardScores,
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17 StandardScoresN, Standardize, Sum, SumOfSquares, TrimMean, Variance,
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18 VarianceN
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19
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20 METHODS
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21 Average
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22 $Value = Average(\@DataArray);
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23
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24 Computes the mean of an array of numbers: SUM( x[i] ) / n
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25
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26 AverageDeviation
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27 $Value = AverageDeviation(\@DataArray);
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28
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29 Computes the average of the absolute deviation of an array of
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30 numbers: SUM( ABS(x[i] - Xmean) ) / n
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31
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32 Correlation
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33 $Value = Correlation(\@XDataArray, \@YDataArray);
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34
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35 Computes the Pearson correlation coefficient between two arrays of
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36 numbers: SUM( (x[i] - Xmean)(y[i] - Ymean) ) / SQRT( SUM( (x[i] -
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37 Xmean)^2 )(SUM( (y[i] - Ymean)^2 )) )
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38
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39 Euclidean
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40 $Return = Euclidean(\@DataArray);
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41
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42 Computes the euclidean distance of an array of numbers: SQRT( SUM(
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43 x[i] ** 2) )
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44
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45 Covariance
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46 $Value = Covariance(\@XDataArray, \@YDataArray);
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47
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48 Computes the covariance between two arrays of numbers: SUM( (x[i] -
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49 Xmean) (y[i] - Ymean) ) / n
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50
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51 Factorial
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52 $Value = Factorial($Num);
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53
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54 Computes the factorial of a positive integer.
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55
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56 FactorialDivison
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57 $Value = FactorialDivision($Numerator, $Denominator);
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58
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59 Compute the factorial divison of two positive integers.
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60
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61 Frequency
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62 %FrequencyValues = Frequency(\@DataArray, [$NumOfBins]);
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63 %FrequencyValues = Frequency(\@DataArray, [\@BinRange]);
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64
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65 A hash array is returned with keys and values representing range and
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66 frequency values, respectively. The frequency value for a specific
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67 key corresponds to all the values which are greater than the
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68 previous key and less than or equal to the current key. A key value
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69 representing maximum value is added for generating frequency
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70 distribution for specific number of bins, and whenever the maximum
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71 array value is greater than the maximum specified in bin range, it
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72 is also added to bin range.
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73
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74 GeometricMean
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75 $Value = GeometricMean(\@DataArray);
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76
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77 Computes the geometric mean of an array of numbers: NthROOT(
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78 PRODUCT(x[i]) )
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79
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80 HarmonicMean
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81 $Value = HarmonicMean(\@DataArray);
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82
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83 Computes the harmonic mean of an array of numbers: 1 / ( SUM(1/x[i])
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84 / n )
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85
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86 KLargest
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87 $Value = KLargest(\@DataArray, $KthNumber);
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88
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89 Returns the k-largest value from an array of numbers.
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90
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91 KSmallest
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92 $Value = KSmallest(\@DataArray, $KthNumber);
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93
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94 Returns the k-smallest value from an array of numbers.
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95
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96 Kurtosis
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97 $Value = Kurtosis(\@DataArray);
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98
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99 Computes the kurtosis of an array of numbers: [ {n(n + 1)/(n - 1)(n
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100 - 2)(n - 3)} SUM{ ((x[i] - Xmean)/STDDEV)^4 } ] - {3((n - 1)^2)}/{(n
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101 - 2)(n-3)}
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102
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103 Maximum
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104 $Value = Maximum(\@DataArray);
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105
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106 Returns the largest value from an array of numbers.
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107
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108 Minimum
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109 $Value = Minimum(\@DataArray);
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110
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111 Returns the smallest value from an array of numbers.
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112
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113 Mean
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114 $Value = Mean(\@DataArray);
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115
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116 Computes the mean of an array of numbers: SUM( x[i] ) / n
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117
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118 Median
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119 $Value = Median(\@DataArray);
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120
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121 Computes the median value of an array of numbers. For an even number
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122 array, it's the average of two middle values.
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123
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124 For even values of n: Xsorted[(n - 1)/2 + 1] For odd values of n:
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125 (Xsorted[n/2] + Xsorted[n/2 + 1])/2
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126
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127 Mode
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128 $Value = Mode(\@DataArray);
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129
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130 Returns the most frequently occuring value in an array of numbers.
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131
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132 PearsonCorrelation
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133 $Value = Correlation(\@XDataArray, \@YDataArray);
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134
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135 Computes the Pearson correlation coefficient between two arrays of
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136 numbers: SUM( (x[i] - Xmean)(y[i] - Ymean) ) / SQRT( SUM( (x[i] -
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137 Xmean)^2 )(SUM( (y[i] - Ymean)^2 )) )
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138
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139 Permutations
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140 $PermutationsRef = Permutations(@DataToPermute);
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141
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142 Generate all possible permuations or a specific permutations of
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143 items in an array and return a reference to an array containing
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144 array references to generated permuations.
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145
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146 This alogrithm is based on the example provided by Mark
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147 Jason-Dominus, and is available at CPAN as mjd_permute standalone
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148 script.
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149
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150 Product
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151 $Value = Product(\@DataArray);
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152
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153 Compute the product of an array of numbers.
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154
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155 Range
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156 ($Smallest, $Largest) = Range(\@DataArray);
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157
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158 Return the smallest and largest values from an array of numbers.
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159
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160 RSquare
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161 $Value = RSquare(\@XDataArray, \@YDataArray);
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162
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163 Computes square of the Pearson correlation coefficient between two
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164 arrays of numbers.
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165
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166 Skewness
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167 $Value = Skewness(\@DataArray);
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168
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169 Computes the skewness of an array of numbers: {n/(n - 1)(n - 2)}
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170 SUM{ ((x[i] - Xmean)/STDDEV)^3 }
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171
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172 StandardDeviation
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173 $Value = StandardDeviation(\@DataArray);
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174
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175 Computes the standard deviation of an array of numbers. SQRT ( SUM(
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176 (x[i] - mean)^2 ) / (n - 1) )
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177
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178 StandardDeviationN
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179 $Value = StandardDeviationN(\@DataArray);
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180
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181 Computes the standard deviation of an array of numbers representing
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182 entire population: SQRT ( SUM( (x[i] - mean)^2 ) / n )
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183
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184 StandardError
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185 $Value = StandardError($StandardDeviation, $Count);
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186
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187 Computes the standard error using standard deviation and sample
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188 size.
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189
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190 Standardize
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191 $Value = Standardize($Value, $Mean, $StandardDeviation);
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192
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193 Standardizes the value using mean and standard deviation.
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194
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195 StandardScores
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196 @Values = StandardScores(\@DataArray);
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197
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198 Computes the standard deviation above the mean for an array of
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199 numbers: (x[i] - mean) / (n - 1)
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200
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201 StandardScoresN
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202 @Values = StandardScoresN(\@DataArray);
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203
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204 Computes the standard deviation above the mean for an array of
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205 numbers representing entire population: (x[i] - mean) / n
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206
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207 Sum
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208 $Value = Sum(\@DataArray);
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209
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210 Compute the sum of an array of numbers.
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211
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212 SumOfSquares
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213 $Value = SumOfSquares(\@DataArray);
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214
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215 Computes the sum of an array of numbers.
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216
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217 TrimMean
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218 $Value = TrimMean(\@DataArray, $FractionToExclude));
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219
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220 Computes the mean of an array of numbers by excluding a fraction of
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221 numbers from the top and bottom of the data set.
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222
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223 Variance
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224 $Value = Variance(\@DataArray);
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225
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226 Computes the variance of an array of numbers: SUM( (x[i] - Xmean)^2
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227 / (n - 1) )
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228
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229 VarianceN
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230 $Value = Variance(\@DataArray);
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231
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232 Compute the variance of an array of numbers representing entire
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233 population: SUM( (x[i] - Xmean)^2 / n )
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234
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235 AUTHOR
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236 Manish Sud <msud@san.rr.com>
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237
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238 SEE ALSO
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239 Constants.pm, ConversionsUtil.pm, MathUtil.pm
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240
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241 COPYRIGHT
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242 Copyright (C) 2015 Manish Sud. All rights reserved.
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243
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244 This file is part of MayaChemTools.
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245
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246 MayaChemTools is free software; you can redistribute it and/or modify it
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247 under the terms of the GNU Lesser General Public License as published by
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248 the Free Software Foundation; either version 3 of the License, or (at
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249 your option) any later version.
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250
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