Statistics/Normal distribution: Difference between revisions

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Pairs of normal numbers are generated from pairs of uniform numbers using the [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

<lang stata>clear all

. set obs 100000

set obs 100000

. gen u=runiform()

gen u=runiform()

. gen v=runiform()

gen v=runiform()

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

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

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

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

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

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

. gen z=rnormal()

gen z=rnormal()

~~. summarize~~ x y z

sum x y z

Variable | Obs Mean Std. Dev. Min Max

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y | 100,000 .0017389 1.001586 -4.631144 4.460274

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

. hist x, normal

hist x, normal

. hist y, normal

hist y, normal

. hist z, normal

hist z, normal

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

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

=={{header|Tcl}}==