# rFractionalWishart: Random Fractional Wishart Matrix In rWishart: Random Wishart Matrix Generation

## Description

Generate `n` random matrices, distributed according to the Wishart distribution with parameters `Sigma` and `df`, W_p(Sigma, df).

## Usage

 ```1 2``` ```rFractionalWishart(n, df, Sigma, covariance = FALSE, simplify = "array") ```

## Arguments

 `n` integer: the number of replications. `df` numeric parameter, “degrees of freedom”. `Sigma` positive definite (p * p) “scale” matrix, the matrix parameter of the distribution. `covariance` logical on whether a covariance matrix should be generated `simplify` logical or character string; should the result be simplified to a vector, matrix or higher dimensional array if possible? For `sapply` it must be named and not abbreviated. The default value, `TRUE`, returns a vector or matrix if appropriate, whereas if `simplify = "array"` the result may be an `array` of “rank” (=`length(dim(.))`) one higher than the result of `FUN(X[[i]])`.

## Details

If X_1, ..., X_m is a sample of m independent multivariate Gaussians with mean vector 0, and covariance matrix Sigma, the distribution of M = X'X is W_p(Sigma, m).

## Value

A numeric array of dimension `p * p * n`, where each array is a positive semidefinite matrix, a realization of the Wishart distribution W_p(Sigma, df)

## References

Adhikari, S. (2008). Wishart random matrices in probabilistic structural mechanics. Journal of engineering mechanics, 134(12), doi: 10.1061/(ASCE)0733-9399(2008)134:12(1029).

## Examples

 `1` ```rFractionalWishart(2, 22.5, diag(1, 20)) ```

rWishart documentation built on Nov. 20, 2019, 1:07 a.m.