mtdistribution {lestat}R Documentation

A Multivariate t-Distribution

Description

Creates an object representing a multivariate non-centered t-distribution.

Usage

mtdistribution(expectation = c(0,0), degreesoffreedom = 10000, 
     P = diag(length(expectation)))

Arguments

expectation

A vector of length at least 2 specifying the expectation of the distribution. By default, the vector (0,0).

degreesoffreedom

The degrees of freedom parameter.

P

A matrix of size k×kk\times k, where kk is the length of the expectation vector. P plays a similar role in the multivariate t-distribution as the precision matrix does in the multivariate normal distribution. By default, P is the identity matrix.

Details

If μ\mu is the expectation, ν\nu the degrees of freedom, PP is the last parameter, and kk the dimension, then the probability density function is proportional to

f(x)=exp(ν+(xμ)tP(xμ))(ν+k)/2f(x)=\exp(\nu + (x-\mu)^tP(x-\mu))^{-(\nu+k)/2}

Value

A multivariate t-distribution.

Author(s)

Petter Mostad <mostad@chalmers.se>

See Also

tdistribution, mnormal

Examples

plot(mtdistribution())
plot(mtdistribution(c(1,2,3), 3))
plot(mtdistribution(c(1,2), 3, matrix(c(1, 0.5, 0.5, 1), 2, 2)))

[Package lestat version 1.9 Index]