Statistics/Normal distribution: Difference between revisions

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=={{header|Stata}}==

~~Here,~~ a normal density is added to the histogram for comparison. See '''[http://www.stata.com/help.cgi?histogram histogram]''' in Stata help.

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.

<lang stata>. clear all

. set obs 100000

number of observations (_N) was 0, now 100,000

. gen x=~~rnormal~~()

. gen u=runiform()

. gen v=runiform()

⚫

. summarize x

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

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

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

. gen z=rnormal()

⚫

. summarize x y z

Variable | Obs Mean Std. Dev. Min Max

-------------+---------------------------------------------------------

x | 100,000 -.~~00149~~ .~~9995225~~ -4.~~24247~~ 4.~~057799~~

x | 100,000 .0025861 1.002346 -4.508192 4.164336

y | 100,000 .0017389 1.001586 -4.631144 4.460274

⚫

. hist(x), normal~~</lang>~~

z | 100,000 .005054 .9998861 -5.134265 4.449522

⚫

. hist x, normal

. hist y, normal

. hist z, normal

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

=={{header|Tcl}}==