Bivarnormcdf
Bivarnormcdf-func
Definition:
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[
]=1 ,E[
]=1 and E[XY]=![\rho \rho](../images/Bivarnormcdf_(function)/math-d2606be4e0cd2c9a6179c8f2e3547a85.png)
![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 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](../images/Bivarnormcdf_(function)/math-49a9949efc1fb2546bf541dd3fbd3a8c.png)
Parameters:
- x (intput, double)
- the first argument for which the bivariate Normal distribution function is to be evaluated, x.
![[-\infty ,+\infty] [-\infty ,+\infty]](../images/Bivarnormcdf_(function)/math-dce01579bb6f7629b3426c61d58bcf24.png)
- y (input, double)
- the second argument for which the bivariate Normal distribution function is to be evaluated, y.
![[-\infty ,+\infty] [-\infty ,+\infty]](../images/Bivarnormcdf_(function)/math-dce01579bb6f7629b3426c61d58bcf24.png)
- rho (input,double)
- the correlation coefficent,
. ![,-1\leq \rho \leq 1 ,-1\leq \rho \leq 1](../images/Bivarnormcdf_(function)/math-1b2d5835bbd1d4627e18e993bcab0fe7.png)
- prob (output,double)
- the probability.