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

 From "Steichen, Thomas J." <[email protected]> To <[email protected]> Subject RE: st: RE: std. bivariate nrm. dist. Date Wed, 8 Dec 2004 13:22:46 -0500

```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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