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.