as251Normal {rpact}

Algorithm AS 251: Normal Distribution

Description

Calculates the Multivariate Normal Distribution with Product Correlation Structure published by Charles Dunnett, Algorithm AS 251.1 Appl.Statist. (1989), Vol.38, No.3 doi:10.2307/2347754.

Usage

as251Normal(
  lower,
  upper,
  sigma,
  ...,
  eps = 1e-06,
  errorControl = c("strict", "halvingIntervals"),
  intervalSimpsonsRule = 0
)

Arguments

lower

Lower limits of integration. Array of N dimensions

upper

Upper limits of integration. Array of N dimensions

sigma

Values defining correlation structure. Array of N dimensions

...

Ensures that all arguments (starting from the "...") are to be named and that a warning will be displayed if unknown arguments are passed.

eps

desired accuracy. Defaults to 1e-06

errorControl

error control. If set to 1, strict error control based on fourth derivative is used. If set to zero, error control based on halving intervals is used

intervalSimpsonsRule

Interval width for Simpson's rule. Value of zero caused a default .24 to be used

Details

For a multivariate normal vector with correlation structure defined by rho(i,j) = bpd(i) * bpd(j), computes the probability that the vector falls in a rectangle in n-space with error less than eps.

This function calculates the bdp value from sigma, determines the right inf value and calls mvnprd.