86 lines
2.2 KiB
PowerShell
86 lines
2.2 KiB
PowerShell
# Statistics/Normal distribution
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# Generates normally distributed random numbers with $mean 0 and standard deviation 1
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function Get-RandomNormal {
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return [Math]::Cos(2.0 * [Math]::PI * (Get-Random -Maximum 1.0)) * [Math]::Sqrt(-2.0 * [Math]::Log((Get-Random -Maximum 1.0)))
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}
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function Write-NormalStats {
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param ([uint32]$SampleSize)
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if ($SampleSize -lt 1) {
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return
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}
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$r = [double[]]::new($SampleSize)
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$h = [uint32[]]::new(12) # all zero by default
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$sum = 0.0
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$hSum = 0
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# Generate '$SampleSize' normally distributed random numbers with $mean 0.5 and standard deviation 0.25
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# calculate their $sum
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# and in which box they will fall when drawing the histogram
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$iTo = $SampleSize - 1
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foreach ($i in 0..$iTo) {
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$r[$i] = .5 + $(Get-RandomNormal) / 4.0
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$sum += $r[$i]
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if ($r[$i] -lt 0.0) {
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$h[0]++
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} elseif ($r[$i] -ge 1.0) {
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$h[11]++
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} else {
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$h[[Math]::Ceiling($r[$i] * 10)]++
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}
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}
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foreach ($hItem in $h) {
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$hSum += $hItem
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}
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# adjust one of the $h[] values if necessary to ensure $hSum = $SampleSize
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$adj = $SampleSize - $hSum
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if ($adj -ne 0) {
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$iTo = $h.Length - 1
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foreach ($i in 0..$iTo) {
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$h[$i] += $adj
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if ($h[$i] -ge 0) {
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break
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}
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$h[$i] -= $adj
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}
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}
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$mean = $sum / $SampleSize
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$sum = 0.0
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# Now calculate their standard deviation
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foreach ($rItem in $r) {
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$sum += [Math]::Pow($rItem - $mean, 2)
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}
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$sd = [Math]::Sqrt($sum / $SampleSize)
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# Draw a histogram of the data with interval 0.1
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# If sample size > 300 then normalize histogram to 300
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$scale = 1.0
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if ($SampleSize -gt 300) {
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$scale = 300.0 / $SampleSize
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}
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Write-Output "Sample size $SampleSize"
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Write-Output (' Mean {0,8:N6} SD {1,8:N6}' -f $mean, $sd)
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$i = -1
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foreach ($hItem in $h) {
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if ($i -eq -1) {
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$out = '< 0.00 : '
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} elseif ($i -eq 10) {
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$out = '>=1.00 : '
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} else {
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$out = ' {0,4:N2} : ' -f ($i / 10.0)
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}
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$out += ('{0,5} ' -f $hItem)
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Write-Output ($out + ('*' * [Math]::Round($hItem * $scale)))
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$i++
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}
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}
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Write-NormalStats 100
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Write-Output ""
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Write-NormalStats 1000
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Write-Output ""
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Write-NormalStats 10000
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Write-Output ""
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