Statistics/Normal distribution: Difference between revisions

=={{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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