Stata/Probability Function

The list of probability functions is available by typing in the command editor : h density functions

Useful quantiles
. di invnorm(.975) 1.959964

. di invchi2(1,.95) 3.8414588

Gaussian Distribution
local q975 = invnormal(.975) tw function y = normalden(x), range(-4 4) || , xlabel(, grid) xline( -`q975' `q975') title(PDF Gaussian with 95 % CI) ; gr export W:/normal.png, replace
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The Gaussian distribution with 90,95 and 99 % confidence intervals.

set scheme s2color global ub10 = invnorm(.95) global lb10 = invnorm(.05) global ub5 = invnorm(.975) global lb5 = invnorm(.025) global ub1 = invnorm(.995) global lb1 = invnorm(.005) tw function y=normden(x), range(-4 $lb5) color(red) recast(area) || function y=normden(x), range($ub5 4)   color(red) recast(area) || function y=normden(x), range(-4 4) lstyle(foreground) ||,      ysca(off) xsca(noline) legend(off) xlabel(-4 "-4 sd" -3 "-3 sd" -2 "-2 sd" -1 "-1 sd" 0 "mean"                     1  "1 sd"  2  "2 sd"  3  "3 sd"  4  "4 sd"                     , grid gmin gmax) xtitle("") ;
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Student Distribution
tw function y = tden(1,x), range(-4 4) || function y = tden(2,x), range(-4 4) || function y = tden(5,x), range(-4 4) || function y = tden(10,x), range(-4 4) || function y = tden(30,x), range(-4 4) || function y = normalden(x), range(-4 4) lw(thick) || , xlabel(, grid) legend(cols(5) label(1 "k=1") label(2 "k=2") label(3 "k=5") label(4 "k=10") label(5 "k=30") label(6 "Gaussienne")) title(PDF Student Distribution) ;
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