An R package for Non-Normal Multivariate Distributions: Simulation and Probability Calculations from Multivariate Lomax (Pareto Type II) and Other Related Distributions

Abstract

Convenient and easy-to-use programs are readily available in R to simulate data from and probability calculations for several common multivariate distributions such as normal and t. However, functions for doing so from other less common multivariate distributions, especially those which are asymmetric, are not as readily available, either in R or otherwise. We introduce the R package NonNorMvtDist to generate random numbers from multivariate Lomax distribution, which constitutes a very flexible family of skewed multivariate distributions. Further, by applying certain useful properties of multivariate Lomax distribution, multivariate cases of generalized Lomax, Mardia’s Pareto of Type I, Logistic, Burr, Cook-Johnson’s uniform, F, and inverted beta can be also considered, and random numbers from these distributions can be generated. Methods for the probability and the equicoordinate quantile calculations for all these distributions are then provided. This work substantially enriches the existing R toolbox for nonnormal or nonsymmetric multivariate probability distributions.