Data update

Task/Statistics-Normal-distribution/PowerShell/statistics-normal-distribution.ps1

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