# Percentiles of $Z=\max(X,Y)$, where X and Y are correlated normal random variables

by Dimitriy V. Masterov   Last Updated January 12, 2018 20:19 PM

Suppose $X \sim N(\mu_x,\sigma_x^2)$, $Y \sim N(\mu_y,\sigma_y^2)$, and $Corr(X,Y)=\rho$. I am interested in calculating percentiles of $Z = \max(X,Y)$.

I know how to find the pdf, mean, and variance of $Z$, but I am having trouble solving or finding an approximation for the percentiles. Has this been worked out somewhere in the literature?

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