Distribution Function of the Standard Bivariate Normal

Computes the cumulative distribution function (CDF) of the standard bivariate normal distribution with specified lower and upper integration limits and correlation coefficient.

Usage

pbvnorm(lower = NA_real_, upper = NA_real_, rho = 0)

Arguments

lower

A numeric vector of length 2 specifying the lower limits of integration.

upper

A numeric vector of length 2 specifying the upper limits of integration.

rho

A numeric value specifying the correlation coefficient of the standard bivariate normal distribution.

Value

A numeric value representing the probability that a standard bivariate normal vector falls within the specified rectangular region.

Details

This function evaluates the probability \(P(\code{lower[1]} < X < \code{upper[1]}, \code{lower[2]} < Y < \code{upper[2]})\) where \((X, Y)\) follows a standard bivariate normal distribution with correlation corr.

Author

Kaifeng Lu, kaifenglu@gmail.com

Examples

pbvnorm(c(-1, -1), c(1, 1), 0.5)
#> [1] 0.4979718