3.5.3.2.3 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.