Phi2rho (version 1.0.1)

Phi2rho-package: Owen's T Function and Bivariate Normal Integral

Description

Computes the Owen's T function or the bivariate normal integral.

Author

Janez Komelj

Maintainer: Janez Komelj <[e-mail]>

Details

The DESCRIPTION file:

Package: Phi2rho
Type: Package
Title: Owen's T Function and Bivariate Normal Integral
Version: 1.0.1
Date: 2023-12-06
Authors@R: person("Janez","Komelj", role = c("aut","cre"),
email = "[e-mail]")
Depends: R (>= 3.5.0), stats
Imports: Rmpfr
Description: Computes the Owen's T function or the bivariate
normal integral using one of the following:
modified Euler's arctangent series, tetrachoric
series, or Vasicek's series. For the methods,
see Komelj, J. (2023) <doi:10.4236/ajcm.2023.134026>
(or reprint <arXiv:2312.00011> with better typography)
and Vasicek, O. A. (1998) <doi:10.21314/JCF.1998.015>.
License: GPL-2 | GPL-3

References

Komelj, J. (2023): The Bivariate Normal Integral via Owen's T Function as a Modified Euler's Arctangent Series, American Journal of Computational Mathematics, 13, 4, 476--504, tools:::Rd_expr_doi("10.4236/ajcm.2023.134026") (or reprint https://arxiv.org/pdf/2312.00011.pdf with better typography).

Owen, D. B. (1956): Tables for Computing Bivariate Normal Probabilities, The Annals of Mathematical Statistics, 27, 4, 1075--1090, tools:::Rd_expr_doi("10.1214/aoms/1177728074").

Owen, D. B. (1980): A table of normal integrals, Communications in Statistics -- Simulation and Computation, 9, 4, 389--419, tools:::Rd_expr_doi("10.1080/03610918008812164").

Vasicek, O. A. (1998): A series expansion for the bivariate normal integral, The Journal of Computational Finance, 1, 4, 5--10, tools:::Rd_expr_doi("10.21314/JCF.1998.015").

Examples

OwenT(2, 0.5)
OwenT(2, 0.5, fun = "mOwenT") # modified arctangent series (default)
OwenT(2, 0.5, fun = "tOwenT") # tetrachoric series
OwenT(2, 0.5, fun = "vOwenT") # Vasicek's series

rho <- 0.6
a <- rho/sqrt(1 - rho^2)
OwenT(0.3, a)
OwenT(0.3, a, fun = "tOwenT") 
OwenT(c(-1, 0.5, 4), a, fun = "vOwenT")

OwenT(2, c(-1, -0.5, 0, 0.5, 1), fun = "vOwenT")

Phi2xy(2, 1.3, 0.5) 
Phi2xy(-2, 0.5, -0.3, fun = "tOwenT")
Phi2xy(c(1, 2, -1.5), c(-1, 1, 2.3), 0.5, fun = "vOwenT")
Phi2xy(1, 2, c(-1, -0.5, 0, 0.5, 1))
Phi2xy(c(1, 2), c(-1,3), c(-0.5, 0.8))