# mtdistribution: A Multivariate t-Distribution In lestat: A Package for Learning Statistics

## Description

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

## Usage

 1 2 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 μ is the expectation, ν the degrees of freedom, P is the last parameter, and k the dimension, then the probability density function is proportional to

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

## Value

A multivariate t-distribution.

## Author(s)

tdistribution, mnormal
 1 2 3 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)))