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Subject: Re: verification of bi-variate normal distribution
Date: Sat, 3 Jan 2009 03:37:02 +0000 (UTC)
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Cris <xiaosong.ding@gmail.com> wrote in message <0d0ff15f-010e-4d8e-81c8-ddf23ca6a04e@w1g2000prk.googlegroups.com>...
> ........
> Thank you both. But any suggestions for the verification of the
> probability when two normally distributed random variables are not
> independent?
> 
> VB
> /Cris

  I'm not sure what you mean in what you call "the verification of the probability".  With your first article Tom interpreted it to mean a verification that for independent variables the results of 'mvncdf' are compatible with those of 'normcdf'.  I took it to mean a verification of the observed joint statistical distribution of your actual variables.  You seemed content with Tom's answer which indicates his was probably the correct interpretation of your query.

  However, the computation of joint normal cumulative probability distributions for correlated random variables is a much more difficult task and cannot be readily found by referring to 'normcdf' values.  There are many algorithms given in the literature for performing this calculation and that used in 'mvncdf' is just one of them.

  The Matlab Statistics Toolbox documentation has a number of references given in the 'mvncdf' function section which you might look up.  You can also peruse the Wikipedia site at

 http://en.wikipedia.org/wiki/Multivariate_normal_distribution

for a discussion of these matters.

Roger Stafford