# Talk:Multivariate t-distribution

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## what is p

What is p? Is it the dimension of $\Sigma$? Albmont 20:07, 6 March 2007 (UTC)

Added a comment to effect that p is the dimension Shaww 09:54, 19 April 2007 (UTC)

## normalization

The bivariate student distribution density function with zero correlation is presented as

$f(t_i) = \frac{1}{2\pi} (1+(t_1^2 + t_2^2)/n)^{-(n+2)/2}.$

But this does not normalize nicely to 1.

$\int_{-\infty}^{\infty} \int_{-\infty}^{\infty} f(t_1,t_2)\,dt_1\,dt_2$≠1

for any n. Only for high n it seems to go to 1.

Where is the (my) mistake?

jasper (talk) 17:06, 21 January 2008 (UTC)

A rough numerical integration with Matlab seem₫s to give an ok normalization to one:
>> p = inline('(1+(x^2+y^2)/n)^( -(n+2)/2 )/(2*pi)')
>> s=0; n=2; for x=-20:0.1:20, for y=-20:0.1:20, s=s+p(n,x,y);end,end,s

the result 99.5946 is approximately 100x0.1x0.1=1. fnielsen (talk) 10:12, 22 January 2008 (UTC)

Sorry, my mistake, fnielsen is right. My infinity was not big enough. Should I delete this entry in the discussion tab? jasper (talk) 16:51, 22 January 2008 (UTC)

I don't think you should delete; errors are good when we learn from them. Now, do the homework: prove analytically that the integral is one: replace $t1 = r \cos \theta , t2 = r \sin \theta \,$ and see what happens :-) Albmont (talk) 13:50, 1 February 2008 (UTC)

This article refers to elliptical distribution theory. I'd like to see a separate article about elliptical distributions. Duoduoduo (talk) 20:01, 11 March 2010 (UTC)