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Statistics/Normal distribution: Difference between revisions
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[nn,xx] = hist(x,100);
bar(xx,nn);</lang>
=={{header|Nim}}==
Nim provides procedures to generate random values following normal distribution and Gauss distribution with given mean and standard deviation.
Here is a way to generate random values following normal distribution from random values following uniform distribution. It uses the Basic form of the Box-Muller transform.
<lang Nim>import math, random, sequtils, stats, strformat, strutils
proc drawHistogram(ns: seq[float]) =
# Distribute values in bins.
const NBins = 50
var minval = min(ns)
var maxval = max(ns)
var h = newSeq[int](NBins + 1)
for n in ns:
let pos = ((n - minval) * NBins / (maxval - minval)).toInt
inc h[pos]
# Eliminate extremes values.
const MaxWidth = 50
let mx = max(h)
var first = 0
while (h[first] / mx * MaxWidth).toInt == 0: inc first
var last = h.high
while (h[last] / mx * MaxWidth).toInt == 0: dec last
# Draw the histogram.
echo ""
for n in first..last:
echo repeat('+', (h[n] / mx * MaxWidth).toInt)
echo ""
const N = 100_000
randomize()
let u1, u2 = newSeqWith(N, rand(1.0))
var z = newSeq[float](N)
for i in 0..<N:
z[i] = sqrt(-2 * ln(u1[i])) * cos(2 * PI * u2[i])
echo &"μ = {z.mean:.12f} σ = {z.standardDeviation:.12f}"
z.drawHistogram()</lang>
{{out}}
<pre>μ = -0.001105836229 σ = 0.999906544722
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</pre>
=={{header|PARI/GP}}==
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