Re: verification of bi-variate normal distribution

On 1月3日, 上午1时28分, "Roger Stafford"
<ellieandrogerxy...@xxxxxxxxxxxxxxxxxxxxxx> wrote:
Cris <xiaosong.d...@xxxxxxxxx> wrote in message <40a781ee-e950-4938-89e6-347193b36...@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>...
in Matlab2008b, there is a function "mvncdf".

suppose I have two random variables. both have standard normal
distributions and they have no covariance (the covariance matrix is an
identity matrix). now I wanna compute the joint probability for these
two variable between -1 and 1.

y = mvncdf(xl,xu,mu,SIGMA) is a good function and can give out the
result.

the question is how I can verify this result because there is no such
a bi-variate normal distribution table as the one for one variable
standard normal distribution to check. before I make use of this
function, I have to make sure that it gives out the correct result.

or some one can provide me with some special cases for bi-variate
normal distributions?

many thanks.

VB
/Cris

I don't see the problem here. The function mvncdf(X,mu,sigma) in which X has rows of two elements each, mu is 1 x 2, and sigma is 2 x 2, gives you precisely the "table" you are looking for. For standard normal the mu's would be zeros and sigma the identity matrix. It is a two-dimensional table, not one-dimensional. Checking that you are in agreement with this table means of course that you have to go beyond the limits of -1 and +1, in principle clear to plus and minus infinity. Nothing short of this will do the job. If your random variables are in agreement with this cumulative distribution function (an admittedly Herculean task) then they are independent, jointly standard normal random variables.

Roger Stafford

Thank you both. But any suggestions for the verification of the
probability when two normally distributed random variables are not
independent?

VB
/Cris
.

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