sirt (version 1.5-0)

pbivnorm2: Cumulative Function for the Bivariate Normal Distribution

Description

This function evaluates the bivariate normal distribution $\Phi_2 ( x , y ; \rho )$ assuming zero means and unit variances. It uses a simple approximation by Cox and Wermuth (1991) with corrected formulas in Hong (1999).

Usage

pbivnorm2(x, y, rho)

Arguments

x

Vector of $x$ coordinates

y

Vector of $y$ coordinates

rho

Vector of correlations between random normal variates

Value

• Vector of probabilities

References

Cox, D. R., & Wermuth, N. (1991). A simple approximation for bivariate and trivariate normal integrals. International Statistical Review, 59, 263-269. Hong, H. P. (1999). An approximation to bivariate and trivariate normal integrals. Engineering and Environmental Systems, 16, 115-127.

See Also

See also the pbivnorm function in the pbivnorm package.

Examples

library(pbivnorm)
# define input
x <- c(0 , 0 ,  .5 , 1  , 1  )
y <- c( 0 , -.5 ,  1 , 3 , .5 )
rho <- c( .2 , .8 , -.4 , .6 , .5 )
# compare pbivnorm2 and pbivnorm functions
pbiv2 <- pbivnorm2( x = x , y = y , rho = rho )
pbiv <- pbivnorm::pbivnorm(  x ,  y , rho = rho )
max( abs(pbiv-pbiv2))
  ## [1] 0.0030626
round( cbind( x , y , rho ,pbiv, pbiv2 ) , 4 )
  ##          x    y  rho   pbiv  pbiv2
  ##   [1,] 0.0  0.0  0.2 0.2820 0.2821
  ##   [2,] 0.0 -0.5  0.8 0.2778 0.2747
  ##   [3,] 0.5  1.0 -0.4 0.5514 0.5514
  ##   [4,] 1.0  3.0  0.6 0.8412 0.8412
  ##   [5,] 1.0  0.5  0.5 0.6303 0.6304