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124 .\" ========================================================================
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125 .\"
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126 .IX Title "STATISTICSUTIL 1"
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127 .TH STATISTICSUTIL 1 "2015-03-29" "perl v5.14.2" "MayaChemTools"
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128 .\" For nroff, turn off justification. Always turn off hyphenation; it makes
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129 .\" way too many mistakes in technical documents.
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130 .if n .ad l
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131 .nh
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132 .SH "NAME"
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133 StatisticsUtil
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134 .SH "SYNOPSIS"
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135 .IX Header "SYNOPSIS"
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136 use StatisticsUtil;
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137 .PP
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138 use Statistics qw(:all);
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139 .SH "DESCRIPTION"
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140 .IX Header "DESCRIPTION"
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141 \&\fBStatisticsUtil\fR module provides the following functions:
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142 .PP
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143 Average, AverageDeviation, Correlation, Covariance, Euclidean, Factorial,
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144 FactorialDivison, Frequency, GeometricMean, HarmonicMean, KLargest, KSmallest,
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145 Kurtosis, Maximum, Mean, Median, Minimum, Mode, PearsonCorrelation, Permutations,
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146 Product, RSquare, Range, Skewness, StandardDeviation, StandardDeviationN,
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147 StandardError, StandardScores, StandardScoresN, Standardize, Sum, SumOfSquares,
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148 TrimMean, Variance, VarianceN
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149 .SS "\s-1METHODS\s0"
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150 .IX Subsection "METHODS"
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151 .IP "\fBAverage\fR" 4
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152 .IX Item "Average"
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153 .Vb 1
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154 \& $Value = Average(\e@DataArray);
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155 .Ve
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156 .Sp
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157 Computes the mean of an array of numbers: \s-1SUM\s0( x[i] ) / n
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158 .IP "\fBAverageDeviation\fR" 4
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159 .IX Item "AverageDeviation"
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160 .Vb 1
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161 \& $Value = AverageDeviation(\e@DataArray);
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162 .Ve
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163 .Sp
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164 Computes the average of the absolute deviation of an array of numbers: \s-1SUM\s0( \s-1ABS\s0(x[i] \- Xmean) ) / n
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165 .IP "\fBCorrelation\fR" 4
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166 .IX Item "Correlation"
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167 .Vb 1
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168 \& $Value = Correlation(\e@XDataArray, \e@YDataArray);
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169 .Ve
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170 .Sp
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171 Computes the Pearson correlation coefficient between two arrays of numbers:
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172 \&\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 )) )
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173 .IP "\fBEuclidean\fR" 4
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174 .IX Item "Euclidean"
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175 .Vb 1
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176 \& $Return = Euclidean(\e@DataArray);
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177 .Ve
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178 .Sp
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179 Computes the euclidean distance of an array of numbers: \s-1SQRT\s0( \s-1SUM\s0( x[i] ** 2) )
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180 .IP "\fBCovariance\fR" 4
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181 .IX Item "Covariance"
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182 .Vb 1
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183 \& $Value = Covariance(\e@XDataArray, \e@YDataArray);
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184 .Ve
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185 .Sp
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186 Computes the covariance between two arrays of numbers: \s-1SUM\s0( (x[i] \- Xmean) (y[i] \- Ymean) ) / n
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187 .IP "\fBFactorial\fR" 4
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188 .IX Item "Factorial"
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189 .Vb 1
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190 \& $Value = Factorial($Num);
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191 .Ve
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192 .Sp
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193 Computes the factorial of a positive integer.
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194 .IP "\fBFactorialDivison\fR" 4
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195 .IX Item "FactorialDivison"
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196 .Vb 1
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197 \& $Value = FactorialDivision($Numerator, $Denominator);
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198 .Ve
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199 .Sp
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200 Compute the factorial divison of two positive integers.
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201 .IP "\fBFrequency\fR" 4
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202 .IX Item "Frequency"
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203 .Vb 2
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204 \& %FrequencyValues = Frequency(\e@DataArray, [$NumOfBins]);
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205 \& %FrequencyValues = Frequency(\e@DataArray, [\e@BinRange]);
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206 .Ve
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207 .Sp
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208 A hash array is returned with keys and values representing range and frequency values, respectively.
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209 The frequency value for a specific key corresponds to all the values which are greater than
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210 the previous key and less than or equal to the current key. A key value representing maximum value is
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211 added for generating frequency distribution for specific number of bins, and whenever the maximum
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212 array value is greater than the maximum specified in bin range, it is also added to bin range.
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213 .IP "\fBGeometricMean\fR" 4
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214 .IX Item "GeometricMean"
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215 .Vb 1
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216 \& $Value = GeometricMean(\e@DataArray);
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217 .Ve
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218 .Sp
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219 Computes the geometric mean of an array of numbers: NthROOT( \s-1PRODUCT\s0(x[i]) )
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220 .IP "\fBHarmonicMean\fR" 4
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221 .IX Item "HarmonicMean"
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222 .Vb 1
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223 \& $Value = HarmonicMean(\e@DataArray);
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224 .Ve
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225 .Sp
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226 Computes the harmonic mean of an array of numbers: 1 / ( \s-1SUM\s0(1/x[i]) / n )
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227 .IP "\fBKLargest\fR" 4
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228 .IX Item "KLargest"
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229 .Vb 1
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230 \& $Value = KLargest(\e@DataArray, $KthNumber);
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231 .Ve
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232 .Sp
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233 Returns the k\-largest value from an array of numbers.
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234 .IP "\fBKSmallest\fR" 4
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235 .IX Item "KSmallest"
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236 .Vb 1
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237 \& $Value = KSmallest(\e@DataArray, $KthNumber);
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238 .Ve
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239 .Sp
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240 Returns the k\-smallest value from an array of numbers.
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241 .IP "\fBKurtosis\fR" 4
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242 .IX Item "Kurtosis"
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243 .Vb 1
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244 \& $Value = Kurtosis(\e@DataArray);
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245 .Ve
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246 .Sp
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247 Computes the kurtosis of an array of numbers:
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248 [ {n(n + 1)/(n \- 1)(n \- 2)(n \- 3)} SUM{ ((x[i] \- Xmean)/STDDEV)^4 } ] \- {3((n \- 1)^2)}/{(n \- 2)(n\-3)}
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249 .IP "\fBMaximum\fR" 4
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250 .IX Item "Maximum"
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251 .Vb 1
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252 \& $Value = Maximum(\e@DataArray);
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253 .Ve
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254 .Sp
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255 Returns the largest value from an array of numbers.
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256 .IP "\fBMinimum\fR" 4
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257 .IX Item "Minimum"
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258 .Vb 1
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259 \& $Value = Minimum(\e@DataArray);
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260 .Ve
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261 .Sp
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262 Returns the smallest value from an array of numbers.
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263 .IP "\fBMean\fR" 4
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264 .IX Item "Mean"
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265 .Vb 1
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266 \& $Value = Mean(\e@DataArray);
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267 .Ve
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268 .Sp
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269 Computes the mean of an array of numbers: \s-1SUM\s0( x[i] ) / n
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270 .IP "\fBMedian\fR" 4
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271 .IX Item "Median"
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272 .Vb 1
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273 \& $Value = Median(\e@DataArray);
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274 .Ve
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275 .Sp
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276 Computes the median value of an array of numbers. For an even number array, it's
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277 the average of two middle values.
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278 .Sp
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279 For even values of n: Xsorted[(n \- 1)/2 + 1]
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280 For odd values of n: (Xsorted[n/2] + Xsorted[n/2 + 1])/2
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281 .IP "\fBMode\fR" 4
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282 .IX Item "Mode"
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283 .Vb 1
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284 \& $Value = Mode(\e@DataArray);
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285 .Ve
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286 .Sp
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287 Returns the most frequently occuring value in an array of numbers.
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288 .IP "\fBPearsonCorrelation\fR" 4
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289 .IX Item "PearsonCorrelation"
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290 .Vb 1
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291 \& $Value = Correlation(\e@XDataArray, \e@YDataArray);
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292 .Ve
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293 .Sp
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294 Computes the Pearson correlation coefficient between two arrays of numbers:
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295 \&\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 )) )
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296 .IP "\fBPermutations\fR" 4
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297 .IX Item "Permutations"
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298 .Vb 1
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299 \& $PermutationsRef = Permutations(@DataToPermute);
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300 .Ve
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301 .Sp
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302 Generate all possible permuations or a specific permutations of items in an array
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303 and return a reference to an array containing array references to generated permuations.
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304 .Sp
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305 This alogrithm is based on the example provided by Mark Jason-Dominus, and is available
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306 at \s-1CPAN\s0 as mjd_permute standalone script.
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307 .IP "\fBProduct\fR" 4
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308 .IX Item "Product"
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309 .Vb 1
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310 \& $Value = Product(\e@DataArray);
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311 .Ve
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312 .Sp
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313 Compute the product of an array of numbers.
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314 .IP "\fBRange\fR" 4
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315 .IX Item "Range"
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316 .Vb 1
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317 \& ($Smallest, $Largest) = Range(\e@DataArray);
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318 .Ve
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319 .Sp
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320 Return the smallest and largest values from an array of numbers.
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321 .IP "\fBRSquare\fR" 4
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322 .IX Item "RSquare"
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323 .Vb 1
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324 \& $Value = RSquare(\e@XDataArray, \e@YDataArray);
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325 .Ve
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326 .Sp
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327 Computes square of the Pearson correlation coefficient between two arrays of numbers.
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328 .IP "\fBSkewness\fR" 4
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329 .IX Item "Skewness"
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330 .Vb 1
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331 \& $Value = Skewness(\e@DataArray);
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332 .Ve
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333 .Sp
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334 Computes the skewness of an array of numbers:
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335 {n/(n \- 1)(n \- 2)} SUM{ ((x[i] \- Xmean)/STDDEV)^3 }
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336 .IP "\fBStandardDeviation\fR" 4
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337 .IX Item "StandardDeviation"
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338 .Vb 1
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339 \& $Value = StandardDeviation(\e@DataArray);
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340 .Ve
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341 .Sp
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342 Computes the standard deviation of an array of numbers.
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343 \&\s-1SQRT\s0 ( \s-1SUM\s0( (x[i] \- mean)^2 ) / (n \- 1) )
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344 .IP "\fBStandardDeviationN\fR" 4
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345 .IX Item "StandardDeviationN"
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346 .Vb 1
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347 \& $Value = StandardDeviationN(\e@DataArray);
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348 .Ve
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349 .Sp
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350 Computes the standard deviation of an array of numbers representing entire population:
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351 \&\s-1SQRT\s0 ( \s-1SUM\s0( (x[i] \- mean)^2 ) / n )
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352 .IP "\fBStandardError\fR" 4
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353 .IX Item "StandardError"
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354 .Vb 1
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355 \& $Value = StandardError($StandardDeviation, $Count);
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356 .Ve
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357 .Sp
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358 Computes the standard error using standard deviation and sample size.
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359 .IP "\fBStandardize\fR" 4
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360 .IX Item "Standardize"
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361 .Vb 1
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362 \& $Value = Standardize($Value, $Mean, $StandardDeviation);
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363 .Ve
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364 .Sp
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365 Standardizes the value using mean and standard deviation.
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366 .IP "\fBStandardScores\fR" 4
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367 .IX Item "StandardScores"
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368 .Vb 1
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369 \& @Values = StandardScores(\e@DataArray);
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370 .Ve
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371 .Sp
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372 Computes the standard deviation above the mean for an array of numbers:
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373 (x[i] \- mean) / (n \- 1)
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374 .IP "\fBStandardScoresN\fR" 4
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375 .IX Item "StandardScoresN"
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376 .Vb 1
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377 \& @Values = StandardScoresN(\e@DataArray);
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378 .Ve
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379 .Sp
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380 Computes the standard deviation above the mean for an array of numbers representing entire population:
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381 (x[i] \- mean) / n
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382 .IP "\fBSum\fR" 4
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383 .IX Item "Sum"
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384 .Vb 1
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385 \& $Value = Sum(\e@DataArray);
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386 .Ve
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387 .Sp
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388 Compute the sum of an array of numbers.
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389 .IP "\fBSumOfSquares\fR" 4
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390 .IX Item "SumOfSquares"
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391 .Vb 1
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392 \& $Value = SumOfSquares(\e@DataArray);
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393 .Ve
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394 .Sp
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395 Computes the sum of an array of numbers.
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396 .IP "\fBTrimMean\fR" 4
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397 .IX Item "TrimMean"
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398 .Vb 1
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399 \& $Value = TrimMean(\e@DataArray, $FractionToExclude));
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400 .Ve
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401 .Sp
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402 Computes the mean of an array of numbers by excluding a fraction of
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403 numbers from the top and bottom of the data set.
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404 .IP "\fBVariance\fR" 4
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405 .IX Item "Variance"
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406 .Vb 1
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407 \& $Value = Variance(\e@DataArray);
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408 .Ve
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409 .Sp
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410 Computes the variance of an array of numbers: \s-1SUM\s0( (x[i] \- Xmean)^2 / (n \- 1) )
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411 .IP "\fBVarianceN\fR" 4
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412 .IX Item "VarianceN"
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413 .Vb 1
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414 \& $Value = Variance(\e@DataArray);
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415 .Ve
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416 .Sp
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417 Compute the variance of an array of numbers representing entire population:
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418 \&\s-1SUM\s0( (x[i] \- Xmean)^2 / n )
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419 .SH "AUTHOR"
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420 .IX Header "AUTHOR"
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421 Manish Sud <msud@san.rr.com>
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422 .SH "SEE ALSO"
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423 .IX Header "SEE ALSO"
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424 Constants.pm, ConversionsUtil.pm, MathUtil.pm
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425 .SH "COPYRIGHT"
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426 .IX Header "COPYRIGHT"
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427 Copyright (C) 2015 Manish Sud. All rights reserved.
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428 .PP
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429 This file is part of MayaChemTools.
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430 .PP
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431 MayaChemTools is free software; you can redistribute it and/or modify it under
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432 the terms of the \s-1GNU\s0 Lesser General Public License as published by the Free
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433 Software Foundation; either version 3 of the License, or (at your option)
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434 any later version.
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