dWishart {CholWishart} R Documentation

## Density for Random Wishart Distributed Matrices

### Description

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

### Usage

```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

```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)
```

[Package CholWishart version 1.1.0 Index]