/* 

	This file: chi2dist.do
      by: Coye Cheshire

	For fun, lets show how a chi-square
	distribution works.
*/

*First, I need to use a lot more memory for stata since I will need a
*million cases.  If you dont have at least a few gigs of ram, you may
*need to reduce the n in my examples below.

*set memory to use 1 gig

set mem 1g

*Now, lets create two random variables, each from a normal distribution.
*We will draw a million cases.

drawnorm x1 x2, n(1000000)

*Following our understanding of a chi-square distribution, we should
*sum the squares of these variables.

gen twovars = x1^2 + x2^2

*Ok, now lets get the summary stats and view the histogram for this
*new "sum of squares" variable.

sum twovars
hist twovars
graph save chi_twovars

*Interesting...that looks a lot like what the chi-square distribution
*is supposed to look like for df=1. Lets try again with 6 total variables.  
*I will make 4 more variables, also drawn randomly from a normal distribution.

drawnorm x3 x4 x5 x6, n(1000000)

* sum the squares.

gen sixvars = x1^2 + x2^2 + x3^2 + x4^2 + x5^2 + x6^2

* summary stats and histogram.

sum sixvars
hist sixvars
graph save chi_sixvars


* Now lets try it one more time with 10 variables.


drawnorm x7 x8 x9 x10, n(1000000)

*Again, lets sum the squares.

gen tenvars = x1^2 + x2^2 + x3^2 + x4^2 + x5^2 + x6^2 + x7^2 +x8^2 ///
+ x9^2 +x10^2

*And we now check the distribution and the summary stats.

sum tenvars
hist tenvars
graph save chi_tenvars

* This last little feature lets us easily combine our three saved graphs
* into one graph.

graph combine chi_twovars.gph chi_sixvars.gph chi_tenvars.gph

exit.