[R] bivariate normal cdf and rho

[Jun Yan]

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).

I explored it using the function pmvnorm in package mvtnorm with
different x and y. The plot suggests the statement may be true. But I can
not prove it analytically after a few days thinking.

I would appreciate if people on the list can point me to the 
references. 

Jun

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