dmtd {mstudentd} | R Documentation |
Density of a Multivariate
Distribution
Description
Density of the multivariate ( variables)
distribution (MTD)
with degrees of freedom
nu
, mean vector mu
and
correlation matrix Sigma
.
Usage
dmtd(x, nu, mu, Sigma, tol = 1e-6)
Arguments
x |
length |
nu |
numeric. The degrees of freedom. |
mu |
length |
Sigma |
symmetric, positive-definite square matrix of order |
tol |
tolerance (relative to largest variance) for numerical lack of positive-definiteness in Sigma. |
Details
The density function of a multivariate distribution
with
variables is given by:
When (univariate case) it becomes:
Value
The value of the density.
Author(s)
Pierre Santagostini, Nizar Bouhlel
References
S. Kotz and Saralees Nadarajah (2004), Multivariate Distributions and Their Applications, Cambridge University Press.
Examples
nu <- 1
mu <- c(0, 1, 4)
Sigma <- matrix(c(0.8, 0.3, 0.2, 0.3, 0.2, 0.1, 0.2, 0.1, 0.2), nrow = 3)
dmtd(c(0, 1, 4), nu, mu, Sigma)
dmtd(c(1, 2, 3), nu, mu, Sigma)
# Univariate
dmtd(1, 3, 0, 1)
dt(1, 3)
[Package mstudentd version 1.1.1 Index]