# rWishart

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##### Random Wishart Matrix Generation

An expansion of R's 'stats' random wishart matrix generation. This package allows the user to generate singular, Uhlig and Harald (1994) <doi:10.1214/aos/1176325375>, and pseudo wishart, Diaz-Garcia, et al.(1997) <doi:10.1006/jmva.1997.1689>, matrices. In addition the user can generate wishart matrices with fractional degrees of freedom, Adhikari (2008) <doi:10.1061/(ASCE)0733-9399(2008)134:12(1029)>, commonly used in volatility modeling. Users can also use this package to create random covariance matrices.

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

##### Usage
rWishart(n, df, Sigma, covariance = FALSE, simplify = "array")
##### Arguments
n

integer: the number of replications.

df

numeric parameter, “degrees of freedom”.

Sigma

positive definite ($p\times p$) “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)

##### Aliases
• rWishart
• rWishart-package
• rWishart
##### Examples
# NOT RUN {
rWishart(2, 5, diag(1, 20))
# }

Documentation reproduced from package rWishart, version 0.1.1, License: GPL-2

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