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MultiStatM (version 2.0.0)

Multivariate Statistical Methods

Description

Algorithms to build set partitions and commutator matrices and their use in the construction of multivariate d-Hermite polynomials; estimation and derivation of theoretical vector moments and vector cumulants of multivariate distributions; conversion formulae for multivariate moments and cumulants. Applications to estimation and derivation of multivariate measures of skewness and kurtosis; estimation and derivation of asymptotic covariances for d-variate Hermite polynomials, multivariate moments and cumulants and measures of skewness and kurtosis. The formulae implemented are discussed in Terdik (2021, ISBN:9783030813925), "Multivariate Statistical Methods".

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Version

Install

install.packages('MultiStatM')

Monthly Downloads

244

Version

2.0.0

License

GPL-3

Maintainer

Emanuele Taufer

Last Published

July 26th, 2024

Functions in MultiStatM (2.0.0)

Convert cumulants to moments (univariate and multivariate)

Standardize multivariate data

Hermite Polynomials (Univariate and Multivariate)

Inverse Hermite Polynomial

Moments and cumulants Uniform Distribution on the Sphere

Estimation of multivariate Mean, Variance, T-Skewness and T-Kurtosis vectors

Moments and cumulants d-variate Skew Normal

Gram-Charlier approximation to a multivariate density

EVSK multivariate Skew Normal

Random multivariate CFUSN

Convert moments to cumulants (univariate and multivariate)

General Partition Function

Moments and Cumulants of the Central Folded Normal Distribution

Moments and cumulants CFUSN

Univariate moments and cumulants from T-vectors

Symmetrizer Matrix

PartitionTypeAll

Partitions, type and number of partitions

Inverse of a Permutation

Random multivariate CFUSSD

SampleVarianceSkewKurt

Estimated Variance of skewness and kurtosis vectors

Symmetrizing vector

Random Multivariate Skew Normal

Estimation of multivariate T-Moments and T-Cumulants

Estimation of Sample Skewness (Mardia, MRSz)

Estimate the N-th d-variate Hermite polynomial

Qplication vector

Random Uniform on the sphere

Asymptotic Variance of the estimated kurtosis vector

Qplication Matrix

Asymptotic Variance of the estimated skewness vector

Estimation of Sample Kurtosis (Mardia, MRSz, Total)

Elimination Matrix

Coefficients of Hermite polynomials

Commutator Index

Commutator Matrix

Distinct values selection vector

Covariance matrix for multivariate T-Hermite polynomials

EVSK of the Uniform distribution on the sphere or its modulus