# dWishart: Density for Random Wishart Distributed Matrices In CholWishart: Cholesky Decomposition of the Wishart Distribution

## Description

Compute the density of an observation of a random Wishart distributed matrix (`dWishart`) or an observation from the inverse Wishart distribution (`dInvWishart`).

## Usage

 ```1 2 3``` ```dWishart(x, df, Sigma, log = TRUE) dInvWishart(x, df, Sigma, log = TRUE) ```

## Arguments

 `x` positive definite p * p observations for density estimation - either one matrix or a 3-D array. `df` numeric parameter, "degrees of freedom". `Sigma` positive definite p * p "scale" matrix, the matrix parameter of the distribution. `log` logical, whether to return value on the log scale.

## Details

Note there are different ways of parameterizing the Inverse Wishart distribution, so check which one you need. Here, If X ~ IW_p(Sigma, df) then X^{-1} ~ W_p(Sigma^{-1}, df). Dawid (1981) has a different definition: if X ~ W_p(Sigma^{-1}, df) and df > p - 1, then X^{-1} = Y ~ IW(Sigma, delta), where delta = df - p + 1.

## Value

Density or log of density

## Functions

• `dInvWishart`: density for the inverse Wishart distribution.

## References

Dawid, A. (1981). Some Matrix-Variate Distribution Theory: Notational Considerations and a Bayesian Application. Biometrika, 68(1), 265-274. doi: 10.2307/2335827

Gupta, A. K. and D. K. Nagar (1999). Matrix variate distributions. Chapman and Hall.

Mardia, K. V., J. T. Kent, and J. M. Bibby (1979) Multivariate Analysis, London: Academic Press.

## Examples

 ```1 2 3 4 5``` ```set.seed(20180222) A <- rWishart(1, 10, diag(4))[, , 1] A dWishart(x = A, df = 10, Sigma = diag(4L), log = TRUE) dInvWishart(x = solve(A), df = 10, Sigma = diag(4L), log = TRUE) ```

CholWishart documentation built on Oct. 8, 2021, 9:09 a.m.