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3.5.3.1.3 Bivarnormcdf
Definition:
/math-2e6eee007fc11c2f764ee24b5349d1ba.png?v=0 "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[/math-75299c2520ca389119694b3da7cc7a84.png?v=0 "X^2")
]=1 ,E[/math-f3e957abe66ba327ad5d300283980b7b.png?v=0 "Y^2")
]=1 and E[XY]=/math-d2606be4e0cd2c9a6179c8f2e3547a85.png?v=0 "\rho")
/math-49a9949efc1fb2546bf541dd3fbd3a8c.png?v=0 "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]](/labtalk/de/images/Bivarnormcdf_(function)/math-dce01579bb6f7629b3426c61d58bcf24.png?v=0 "[-\infty ,+\infty]")
- y (input, double)
- the second argument for which the bivariate Normal distribution function is to be evaluated, y.
- rho (input,double)
- the correlation coefficent, .
/math-1b2d5835bbd1d4627e18e993bcab0fe7.png?v=0 ",-1\leq \rho \leq 1")
- prob (output,double)
- the probability.