hgm.ncorthant: The function hgm.ncorthant evaluates the orthant probability. In hgm: Holonomic Gradient Method and Gradient Descent

Description

The function hgm.ncorthant evaluates the orthant probability, which is the normalization constant of the multivariate normal distribution restrcted to the first orthant.

Usage

 `1` ```hgm.ncorthant(x,y,rk_step_size=1e-3) ```

Arguments

 `x` See the description of y. `y` This function evaluates the orthant probability for the m dimensional multivariate normal distribution whose m by m covariance matrix and the mean vector of size m are x and y respectively. `rk_step_size` The step size for the Runge-Kutta method to apply the HGM.

Details

The function hgm.ncorthant evaluates the orthant probability, which is the normalization constant of the m-dimensional multivariate normal distribution restrcted to the first orthant. It uses the holonomic gradient method (HGM) to evalute it. The rank of the system of differential equations for the HGM is 2^m.

Value

The output is the orthant probalibity.

Tamio Koyama

References

Tamio Koyama, Akimichi Takemura, Calculation of orthant probabilities by the holonomic gradient method, http://arxiv.org/abs/1211.6822.

Examples

 ```1 2 3 4 5 6 7 8 9``` ```## ===================================================== ## Example 1. Computing the orthant probability ## ===================================================== x <- matrix(c(15,26,23,19, 26,47,46,35, 23,46,65,38, 19,35,38,33), nrow =4) y <- c(1,2,3,4) hgm.ncorthant(x,y) ```

hgm documentation built on May 30, 2017, 8:17 a.m.