cmvnorm-package {cmvnorm}

The Complex Multivariate Gaussian Distribution

Description

Various utilities for the complex multivariate Gaussian distribution and complex Gaussian processes.

Details

The DESCRIPTION file:

Package:	cmvnorm
Type:	Package
Title:	The Complex Multivariate Gaussian Distribution
Version:	1.0-7
Authors@R:	person(given=c("Robin", "K. S."), family="Hankin", role = c("aut","cre"), email="[e-mail]", comment = c(ORCID = "0000-0001-5982-0415"))
Depends:	emulator (>= 1.2-21)
Suggests:	knitr
Imports:	elliptic
Maintainer:	Robin K. S. Hankin <[e-mail]>
Description:	Various utilities for the complex multivariate Gaussian distribution and complex Gaussian processes.
VignetteBuilder:	knitr
License:	GPL-2
URL:	https://github.com/RobinHankin/cmvnorm
BugReports:	https://github.com/RobinHankin/cmvnorm/issues
Author:	Robin K. S. Hankin [aut, cre] (<https://orcid.org/0000-0001-5982-0415>)

Index of help topics:

Im<-                    Manipulate real or imaginary components of an
                        object
Mvcnorm                 Multivariate complex Gaussian density and
                        random deviates
cmvnorm-package         The Complex Multivariate Gaussian Distribution
corr_complex            Complex Gaussian processes
isHermitian             Is a Matrix Hermitian?
var                     Variance and standard deviation of complex
                        vectors
wishart                 The complex Wishart distribution

Generalizing the real multivariate Gaussian distribution to the complex case is not straightforward but one common approach is to replace the real symmetric variance matrix with a Hermitian positive-definite matrix. The cmvnorm package provides some functionality for the resulting density function.

Author(s)

NA

Maintainer: Robin K. S. Hankin <[e-mail]>

References

• N. R. Goodman 1963. “Statistical analysis based on a certain multivariate complex Gaussian distribution”. The Annals of Mathematical Statistics. 34(1): 152–177

• R. K. S. Hankin 2015. “The complex multivariate Gaussian distribution”. R News, volume 7, number 1.

Examples

S1 <- 4+diag(5)
S2 <- S1
S2[1,5] <- 4+1i
S2[5,1] <- 4-1i   # Hermitian


rcmvnorm(10,sigma=S1)
rcmvnorm(10,mean=rep(1i,5),sigma=S2)

dcmvnorm(rep(1,5),sigma=S2)