mtdistribution {lestat}

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\times k, where k 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 \mu is the expectation, \nu the degrees of freedom, P is the last parameter, and k the dimension, then the probability density function is proportional to

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

Value

A multivariate t-distribution.

Author(s)

Petter Mostad <[e-mail]>

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)))