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From: Cris <xiaosong.ding@gmail.com>
Newsgroups: comp.soft-sys.matlab
Subject: Re: verification of bi-variate normal distribution
Date: Fri, 2 Jan 2009 20:41:08 -0800 (PST)
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On 1=D4=C23=C8=D5, =C9=CF=CE=E711=CA=B137=B7=D6, "Roger Stafford"
<ellieandrogerxy...@mindspring.com.invalid> wrote:
> Cris <xiaosong.d...@gmail.com> wrote in message <0d0ff15f-010e-4d8e-81c8-=
ddf23ca6a...@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 pr=
obability".  With your first article Tom interpreted it to mean a verificat=
ion that for independent variables the results of 'mvncdf' are compatible w=
ith those of 'normcdf'.  I took it to mean a verification of the observed j=
oint statistical distribution of your actual variables.  You seemed content=
 with Tom's answer which indicates his was probably the correct interpretat=
ion of your query.
>
>   However, the computation of joint normal cumulative probability distrib=
utions for correlated random variables is a much more difficult task and ca=
nnot be readily found by referring to 'normcdf' values.  There are many alg=
orithms given in the literature for performing this calculation and that us=
ed 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 al=
so peruse the Wikipedia site at
>
>  http://en.wikipedia.org/wiki/Multivariate_normal_distribution
>
> for a discussion of these matters.
>
> Roger Stafford

Thank you, Roger.

You are right. Tom solved part of my puzzles when two random variables
are independent. My second question is just as what you have described
above. Maybe it is really hard to verify the results of the
probability for correlated random variables. I'd better search the
literature...

VB
/Cris