Evaluates the bivariate normal cumulative probability distribution function.

Namespace: Imsl.Stat
Assembly: ImslCS (in ImslCS.dll) Version: 6.5.0.0

Syntax

C#
public static double BivariateNormal(
	double x,
	double y,
	double rho
)
Visual Basic (Declaration)
Public Shared Function BivariateNormal ( _
	x As Double, _
	y As Double, _
	rho As Double _
) As Double
Visual C++
public:
static double BivariateNormal(
	double x, 
	double y, 
	double rho
)

Parameters

x
Type: System..::.Double
The x-coordinate of the point for which the bivariate normal distribution function is to be evaluated.
y
Type: System..::.Double
The y-coordinate of the point for which the bivariate normal distribution function is to be evaluated.
rho
Type: System..::.Double
The correlation coefficient.

Return Value

The probability that a bivariate normal random variable (X,Y) with correlation rho satisfies X\le{\tt x} and Y\le{\tt y} .

Remarks

Let (X,Y) be a bivariate normal variable with mean (0,0) and variance-covariance matrix

\left[\begin{array}{cc}1&\rho\\\rho &1\end{array}\right]

This method computes the probability that X\le{ \tt x} and Y\le{\tt y}.

Plot of Bivariate Normal Distribution Function

See Also