Title: Random Wishart Matrix Generation
Version: 0.1.2
Maintainer: Ben Barnard <benbarnard87@gmail.com>
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.
Depends: R (≥ 3.3)
Imports: Matrix, MASS, stats, lazyeval
License: GPL-2
Encoding: UTF-8
LazyData: true
RoxygenNote: 6.1.1
Suggests: covr, knitr, rmarkdown, testthat
URL: https://rwishart.bearstatistics.com
NeedsCompilation: no
Packaged: 2019-11-19 19:46:52 UTC; ben_b
Author: Ben Barnard [aut, cre], Dean Young [aut]
Repository: CRAN
Date/Publication: 2019-11-19 23:10:02 UTC

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))

Fractional Wishart Helper Function

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

FractionalWishart(df, Sigma, covariance = FALSE)

Arguments

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

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

FractionalWishart(22.5, diag(1, 20))

Nonsingular Wishart Helper Function

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

NonsingularWishart(df, Sigma, covariance = FALSE)

Arguments

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

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

NonsingularWishart(20, diag(1,5))

Psuedo Wishart Helper Function

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

PsuedoWishart(df, Sigma, covariance = FALSE)

Arguments

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

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

PsuedoWishart(5, diag(1, 20))

Singular Wishart Helper Function

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

SingularWishart(df, Sigma, covariance = FALSE)

Arguments

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

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

SingularWishart(5, diag(1, 20))

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))

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))

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))

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))

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))