[R] bivariate normal cdf and rho

[Thomas Lumley]

On Wed, 1 May 2002, Jun Yan wrote:

> 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).
>

It is true.  You want references to the tetrachoric correlation.  The
tetrachoric correlation is the estimate of rho based on F(x,y), and it
wouldn't be any use if it weren't 1-1. I don't have any specific
references. I tried Kendall & Stuart, but it doesn't give details.

	-thomas

Thomas Lumley			Asst. Professor, Biostatistics
tlumley at u.washington.edu	University of Washington, Seattle

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