# dT: Density function for (multivariate) t distribution In bbricks: Bayesian Methods and Graphical Model Structures for Statistical Modeling

## Description

Get the density of a set of samples from a t distribution. For a random vector x, the density function is defined as:

Gamma((df + p)/2) / (Gamma(df/2)df^{p/2} pi ^{p/2} |Sigma|^{1/2}) [1+1/df (x-df)^T Sigma^{-1} (x-df)]^{-(df +p)/2}

Where p is the dimension of x.

## Usage

 `1` ```dT(x, mu, Sigma = NULL, A = NULL, df = 1, LOG = TRUE) ```

## Arguments

 `x` matrix, when x is a numeric vector, it will be converted to a matrix with 1 column! `mu` numeric, mean vector. `Sigma` matrix, Sigma is proportional to the covariance matrix of x, one of Sigma and A should be non-NULL. `A` matrix, the Cholesky decomposition of Sigma, an upper triangular matrix, one of Sigma and A should be non-NULL. `df` numeric, degrees of freedom. `LOG` logical, return log density of LOG=TRUE, default TRUE.

## Value

A numeric vector, the probability densities.

`rT`
 ```1 2 3 4``` ```plot( dT(x=seq(-5,5,length.out = 1000),mu = 0,Sigma = 1,LOG = FALSE) ,type = "l" ) ```