Let $X,Y$ be a bivariate normal distribution with correlation $\rho$, means $\mu_1 \mu_2$ and variances $\sigma_1^2, \sigma_2^2$. Is there an expression for $$P(X \ge 0, Y \ge 0)$$ that only uses $\phi$ and $\Phi$ (density and distribution function of a standard univariate normal) and no integrals?
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Claudio Moneo
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1There is one if $\mu_1=0,\mu_2=0$: https://math.stackexchange.com/q/255368/321264. – StubbornAtom Feb 01 '22 at 14:41