[Date Prev][Date Next][Thread Prev][Thread Next][Date index][Thread index]

From |
Gary Longton <[email protected]> |

To |
[email protected] |

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

Date |
Wed, 08 Dec 2004 13:13:09 -0800 |

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

* * 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/

**References**:**RE: st: RE: std. bivariate nrm. dist.***From:*"Steichen, Thomas J." <[email protected]>

- Prev by Date:
**st: Sample size** - Next by Date:
**st: RE: xtabond machinations** - Previous by thread:
**RE: st: RE: std. bivariate nrm. dist.** - Next by thread:
**RE: st: RE: std. bivariate nrm. dist.** - Index(es):

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