dInvWishart {bbricks} R Documentation

## Density function of Inverse-Wishart distribution

### Description

For a random matrix x, The density function of Inverse-Wishart distribution is defined as:

(2^{(df p)/2} Gamma_p(df/2) |scale|^{-df/2})^{-1} |x|^{(-df-p-1)/2} exp(-1/2 tr(x^{-1} scale))

Where x is a pxp symmetric positive definite matrix, Gamma_p() is the multivariate Gamma function of dimension p.

### Usage

```dInvWishart(x, df, scale, LOG = TRUE)
```

### Arguments

 `x` matrix, a symmetric positive-definite matrix. `df` numeric, the degree of freedom. `scale` matrix, a symmetric positive-definite matrix, the 'scale' parameter. The 'rate' parameter in Wishart is the 'scale' parameter in InvWishart. `LOG` logical, return log density of LOG=TRUE, default TRUE.

### Value

A numeric vector, the density values.

### References

Wishart, John. "The generalized product moment distribution in samples from a normal multivariate population." Biometrika (1928): 32-52.

MARolA, K. V., JT KBNT, and J. M. Bibly. Multivariate analysis. AcadeInic Press, Londres, 1979.

### Examples

```x <- crossprod(matrix(rnorm(15),5,3)) #generate a symmetric positive-definite matrix
scale <- crossprod(matrix(rnorm(15),5,3)) #the prior scale of x
dInvWishart(x,df = 5,scale = scale,LOG = TRUE)
dInvWishart(x,df = 5,scale = scale,LOG = FALSE)
```

[Package bbricks version 0.1.4 Index]