| Phi2rho-package {Phi2rho} | R Documentation |
Owen's T Function and Bivariate Normal Integral
Description
Computes the Owen's T function or the bivariate normal integral.
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 = "jkomelj@siol.net")
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
Author(s)
Janez Komelj
Maintainer: Janez Komelj <jkomelj@siol.net>
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, 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, doi:10.1214/aoms/1177728074.
Owen, D. B. (1980): A table of normal integrals, Communications in Statistics – Simulation and Computation, 9, 4, 389–419, 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, 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))