Re: st: RE: std. bivariate nrm. dist.

[Gary Longton <glongton@fhcrc.org>]

As an (hopefully easier) alternative, The BVN density formula Tom provides is 
also wrapped in the short program -bnormpdf- on SSC.

 type -ssc describe bnormpdf-

- Gary

Steichen, Thomas J. wrote:


> Fatma Bircan writes:
>
> > I want to calculte the standard bivariate normal distribution 
> > for the two variables with correlation. Say X and Y are my 
> > variables and rho is the correlation term. How do I calculate 
> > the standard bivariate normal distribution function for f(X, 
> > Y, rho) in Stata
>
> This looks like you want the density function...
>
> Given x and y are standardized variables 
>    x = (X-Xbar)/sd(X) and y = (Y-Ybar)/sd(Y) 
> (where Xbar is the mean of X and sd(X) is the standard deviation of X, etc)
> and p = rho
>
> f(x,y,p) = (1 / (2*_pi*sqrt(1-p^2)) * exp( -1/(2*(1-p)) * (x^2 - 2*p*x*y + y^2) )
>
>
> Given unstandardized variables X and Y
>
> f(X,Y,p) = (1 / (2*_pi*sd(X)*sd(Y)*sqrt(1-p^2)) * exp( -1/(2*(1-p)) * 
>   ( ((X-Xbar)/sd(X))^2 - 2*p*(X-Xbar)/sd(X)*(Y-Ybar)/sd(Y) + ((Y-Ybar)/sd(Y))^2 ) )  
> Hope I got all those parentheses in there.
>
> Tom
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