Package 'rWishart'

Random Fractional Wishart Matrix

Description

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

Usage

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

Arguments

n	integer: the number of replications.
df	numeric parameter, “degrees of freedom”.
Sigma	positive definite ($p\times p$) “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)

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

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

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Random Nonsingular Wishart Matrix

Description

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

Usage

rNonsingularWishart(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)

Examples

rNonsingularWishart(2, 20, diag(1, 5))

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Random Psuedo Wishart Matrix

Description

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

Usage

rPsuedoWishart(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)

References

Diaz-Garcia, Jose A, Ramon Gutierrez Jaimez, and Kanti V Mardia. 1997. “Wishart and Pseudo-Wishart Distributions and Some Applications to Shape Theory.” Journal of Multivariate Analysis 63 (1): 73–87. doi:10.1006/jmva.1997.1689.

Examples

rPsuedoWishart(2, 5, diag(1, 20))

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Random Singular Wishart Matrix

Description

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

Usage

rSingularWishart(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)

References

Uhlig, Harald. 1994. “On Singular Wishart and Singular Multivariate Beta Distributions.” The Annals of Statistics 22 (1): 395–405. doi:10.1214/aos/1176325375.

Examples

rSingularWishart(2, 5, diag(1, 20))

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Random Wishart Matrix Generation

Description

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)

Examples

rWishart(2, 5, diag(1, 20))

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Test if Matrix is a Wishart Matrix

Description

Given a random Wishart matrix, B, from W_p(Sigma, df) and independent random vector a, then (a' B a) / (a' Sigma a) is chi-squared with df degrees of freedom.

Usage

wishartTest(WishMat, Sigma, vec = NULL)

Arguments

WishMat	random Wishart Matrix from W_p(Sigma, df)
Sigma	Covariance matrix for W_p(Sigma, df)
vec	independent random vector

Value

A chi-squared random variable with df degrees of freedom.

Examples

wishartTest(rWishart(1, 5, diag(1, 20), simplify = FALSE)[[1]], diag(1, 20))

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