# 3.5.3.1.3 Bivarnormcdf

## Definition:

$prob = bivarnormcdf(x, y, rho)$ computes the lower tail probability for the bivariate Normal distribution.

For the two random variables (X, Y ) following a bivariate Normal distribution with

E[X]=0, E[Y]=0, E[$X^2$]=1 ,E[$Y^2$]=1 and E[XY]=$\rho$

$P(X\leq x,Y\leq y)=\frac 1{2\pi \sqrt{1-\rho ^2}}\int_{-\infty }^y\int_{-\infty }^x\exp (\frac{x^2-2\rho XY+Y^2}{2(1-\rho ^2)})dXdY$

## Parameters:

x (intput, double)
the first argument for which the bivariate Normal distribution function is to be evaluated, x. $[-\infty ,+\infty]$
y (input, double)
the second argument for which the bivariate Normal distribution function is to be evaluated, y. $[-\infty ,+\infty]$
rho (input,double)
the correlation coefficent, $\rho$. $,-1\leq \rho \leq 1$
prob (output,double)
the probability.