Statistics/Normal distribution: Difference between revisions

# Take a uniform random number generator and create a large (you decide how large) set of numbers that follow a normal (Gaussian) distribution. Calculate the dataset's mean and stddevstandard deviation, and show thea histogram hereof the data.

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<langsyntaxhighlight lang="csharp">using System;

}</langsyntaxhighlight>

<langsyntaxhighlight lang="cpp">#include <random>

}</langsyntaxhighlight>

<langsyntaxhighlight lang="d">import std.stdio, std.random, std.math, std.range, std.algorithm,

}</langsyntaxhighlight>

<langsyntaxhighlight lang="elixir">defmodule Statistics do

end)</langsyntaxhighlight>

<langsyntaxhighlight lang="fortran">program Normal_Distribution

end program</langsyntaxhighlight>

<langsyntaxhighlight lang="freebasic">' FB 1.05.0 Win64

Sleep</langsyntaxhighlight>

<langsyntaxhighlight lang="go">package main

}</langsyntaxhighlight>

<langsyntaxhighlight lang="haskell">import Data.Map (Map, empty, insert, findWithDefault, toList)

runTest 2000000</langsyntaxhighlight>

<langsyntaxhighlight lang="j">runif01=: ?@$ 0: NB. random uniform number generator

histogram=: <:@(#/.~)@(i.@#@[ , I.)</langsyntaxhighlight>

<langsyntaxhighlight lang="j"> DataSet=: rnorm01 1e5

plot (5 %~ i: 25) ([;histogram) DataSet</langsyntaxhighlight>

<langsyntaxhighlight lang="java">import static java.lang.Math.*;

}</langsyntaxhighlight>

<langsyntaxhighlight lang="julia">using Printf, Distributions, Gadfly

draw(PNG("norm_hist.png", 10cm, 10cm), h)</langsyntaxhighlight>

<langsyntaxhighlight lang="scala">// version 1.1.2

}</langsyntaxhighlight>

<langsyntaxhighlight Lassolang="lasso">define stat1(a) => {

^}</langsyntaxhighlight>

<langsyntaxhighlight lang="lb">call sample 100000

end function</langsyntaxhighlight>

<langsyntaxhighlight Lualang="lua">function gaussian (mean, variance)

showHistogram(t)</langsyntaxhighlight>

<langsyntaxhighlight lang="maple">with(Statistics):

Histogram( X );</langsyntaxhighlight>

=={{header|Mathematica}}/{{header|Wolfram Language}}==

<langsyntaxhighlight Mathematicalang="mathematica">x:= RandomReal[1]

<langsyntaxhighlight Matlablang="matlab"> N = 100000;

bar(xx,nn);</langsyntaxhighlight>

<langsyntaxhighlight lang="parigp">rnormal()={

my(u1=random(1.),u2=random(1.));

sqrt(-2*log(u1))*cos(2*Pi*u1u2)

show(10^4)</langsyntaxhighlight>

<langsyntaxhighlight lang="parigp">rreal()={

};</langsyntaxhighlight>

<langsyntaxhighlight Clang="c">GEN

}</langsyntaxhighlight>

<langsyntaxhighlight lang="pascal">Program Example40;

end.</langsyntaxhighlight>

{{trans|Perl 6Raku}}

<langsyntaxhighlight lang="perl">use constant pi => 3.14159265;

<langsyntaxhighlight lang="purebasic">Procedure.f randomf(resolution = 2147483647)

EndIf</langsyntaxhighlight>

<langsyntaxhighlight lang="python">from __future__ import division

plt.hist(data,bins=50)</langsyntaxhighlight>

<langsyntaxhighlight lang="racket">

<langsyntaxhighlight lang="racket">

The REXX language doesn't have any "higher math" BIF functions like &nbsp; SIN, COS, LN, LOG, SQRT, EXP, POW, etc,

<langsyntaxhighlight lang="rexx">/*REXX program generates 10,000 normally distributed numbers (Gaussian distribution).*/

numeric digits 20 /*use 20 twenty decimal digitsdigs for accuracy.*/

do j=1 for n; _= #.j; s=s+_; ss=ss+_*_ /*the sum, and the sum of squares. */

say 'number of data points = ' aafmt(n )

say ' minimum = ' aafmt(mn )

say ' maximum = ' aafmt(mx )

say ' arithmetic mean = ' aafmt(s/n)

say ' standard deviation = ' aafmt(sqrt( ss/n - (s/n) **2) )

sdE= sd - 4 /*the effective (useableusable) screen depth. */

do i=1 for n; ?= trunc( (#.i-mn) * $) /*calculate the relative line. */

!.?= !.? + 1 /*bump the counter. /*bump the counter. */

?mn= min(?mn, !.?); ?mx= max(?mx, !.?) /*find the minimum. and maximum*/

f= swE/?mx /*limit graph to 1 full screen*/

do h=0 for sdE; _= !.h /*obtain a data point. */

aafmt: parse arg a@; return left('', (a@>=0) + 2 * datatype(a@, 'W'))a@ /*prepend a blank if #>=0, add 2 blanks if whole.*/

e: e = 2.7182818284590452353602874713526624977572470936999595749669676277240766303535; return e

pi: pi= 3.1415926535897932384626433832795028841971693993751058209749445923078164062862; return pi

r2r: return arg(1) // (pi() * 2) /*normalize the given angle (in radians) to ±2pi.*/

rand: return random(1, 1e5) / 1e5 /*REXX generates uniform random postive integers.*/

ln: procedure; parse arg x,f; call_= e; ig= x>1.5;do isk= 1 -2*(ig\==1); iiiz= 0; xx=*_ x**-is; doif whilek>=0 & (ig & xx>iz<1.5 | \ig & xx<iz>.5) then leave; _= _*_; izz= iz; end; xx= izz

ii= ii +is*2**k; _end; x= x*e**-ii-1; z=0; do k_=-1; izp= xx*_ **-isz; ifdo k>=0 & (ig & iz<1 | \ig & iz>.5) then leave; _= -_*x;z=z+_/k;if izzz=p iz;then leave;p=z;end; return xx= izzz+ii

cos: procedure; parseif arga=hpi x;| xa=r2r(x)hpi*3 then return 0; if a=abs(x);pi/3 hpi= pi*then return .5; numeric fuzz min(6, digits()-3); if a=pi *2/3 then return -.5; z= 1; _= 1

x= x*x; ifp= az; do k=hpi2 | aby 2; _=hpi*3 -_ then* returnx 0/ (k*(k-1)); if a z=pi/3 z then+ return_; .5; if az=pi*2/3p then returnleave; -.5 p= z; end; return .sinCos(1,1,-1)z

sqrt: procedure; parse arg x; if x=0 then return 0; d= digits(); m.= 9; numeric digits; numeric form; h= d+6

parse value format(x,2,1,,0) 'E0' with g 'E' _ .; g=g*.5'e'_%2; do j=0 while h>9; m.j=h; h=h%2+1; end /*j*/

do k=j+5 to 0 by -1; numeric digits m.k; g=(g+x/g)*.5; end /*k*/; numeric digits d; return g/1</langsyntaxhighlight>

The graph is shown at &nbsp; <big>'''³/₄''' &nbsp; size.

<langsyntaxhighlight lang="runbasic">

END</langsyntaxhighlight>

<langsyntaxhighlight lang="sas">data test;

*/</langsyntaxhighlight>

{{trans|Perl 6Raku}}

<langsyntaxhighlight lang="ruby">define τ = NumberNum.tau

var m = (dataset.sum(0) / size)

var σ = sqrt(dataset  »**» 2 -> sum(0) / size - m**2)

dataset.each { |n| hash{ n.round(0) }  := 0 ++ }

}</langsyntaxhighlight>

Pairs of normal numbers are generated from pairs of uniform numbers using the polar form of [https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform Box-Muller method]. A normal density is added to the histogram for comparison. See '''[http://www.stata.com/help.cgi?histogram histogram]''' in Stata help. A [https://en.wikipedia.org/wiki/Q%E2%80%93Q_plot Q-Q plot] is also drawn.

<syntaxhighlight lang ="stata">. clear all

. set obs 100000

. gen u=runiform()

. gen v=runiform()

. gen r=sqrt(-2*log(u))

. gen x=r*cos(2*_pi*v)

. gen y=r*sin(2*_pi*v)

. gen z=rnormal()

. summarizesum x y z

. hist x, normal

. hist y, normal

. hist z, normal

. qqplot x z, msize(tiny)</langsyntaxhighlight>

<langsyntaxhighlight lang="tcl">package require Tcl 8.5

stats 100000 20</langsyntaxhighlight>

<langsyntaxhighlight lang="zkl">fcn norm2{ // Box-Muller

};</langsyntaxhighlight>

<langsyntaxhighlight lang="zkl">foreach i in (N/2){ v1,v2:=norm2(); accum(v1); accum(v2); }

foreach p in (h){ println("*"*(p/SCALE)) }</langsyntaxhighlight>