Bivariate normal distribution

Sander

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Jan 31, 2012
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Does there exist an explicit expression (without integral) for the bivariate normal distribution \(\displaystyle f(s):=P(X<s,Y<s)\) with zeros means and covariance matrix \(\displaystyle \Sigma = \left[\begin{array}{cc}{1 & \rho\\ \rho & 1}\end{array}\right]\) in terms of \(\displaystyle s\) and \(\displaystyle \rho\) (and probably in terms of the univariate standard normal distribution)?
 
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