[R] bivariate normal cdf and rho

[Jun Yan]

A while back, I asked the following quesiton:

> Suppose F(x, y; rho) is the cdf of a bivariate normal distribution, with
> standardized marginals and correlation parameter rho. For any fixed x and
> y, I wonder if F(x, y; rho) is a monotone increasing function of rho,
> i.e., there is a 1 to 1 map from rho to F(x, y; rho).

Actually there is a beautiful result on this and Professor S. Le Cessie
from Netherlands kindly gave me an elegant proof of the following:

	d  F(x, y; rho) / d rho = f(x, y; rho),

where f is the standard bivariate normal density.

It can be proved by showing that 

	d f(x, y; rho) / d rho = d f(x, y; rho) / dx dy.

My thanks to Prof. Thomas Lumley, Chong Gu, and John Fox for pointing me
to the references.

Jun

-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-
r-help mailing list -- Read http://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html
Send "info", "help", or "[un]subscribe"
(in the "body", not the subject !)  To: r-help-request at stat.math.ethz.ch
_._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._