Stata The Stata listserver
[Date Prev][Date Next][Thread Prev][Thread Next][Date index][Thread index]

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

-----------------------------------------
CONFIDENTIALITY NOTE:  This e-mail message, including any  attachment(s),
contains information that may be confidential,  protected by the attorney-
client or other legal privileges, and/or  proprietary non-public
information.  If you are not an intended  recipient of this message or an
authorized assistant to an intended  recipient, please notify the sender by
replying to this message and  then delete it from your system.  Use,
dissemination, distribution,  or reproduction of this message and/or any of
its attachments (if  any) by unintended recipients is not authorized and
may be unlawful.


*
*   For searches and help try:
*   http://www.stata.com/support/faqs/res/findit.html
*   http://www.stata.com/support/statalist/faq
*   http://www.ats.ucla.edu/stat/stata/



© Copyright 1996–2024 StataCorp LLC   |   Terms of use   |   Privacy   |   Contact us   |   What's new   |   Site index