alphastable: An R Package for Modelling Multivariate Stable and Mixture of Symmetric Stable Distributions

TL;DR

The paper introduces the alphastable R package, enabling comprehensive modeling, simulation, and parameter estimation of univariate and multivariate stable distributions, aiding applications in finance and economics.

Contribution

It provides the first comprehensive R package for generating, computing, and estimating parameters of various stable distributions, including mixtures and multivariate cases.

Findings

Efficient algorithms for random number generation from stable distributions.

Accurate computation of density and distribution functions for stable distributions.

Successful application in modeling financial and economic data.

Abstract

The family of stable distributions received extensive applications in many fields of studies since it incorporates both the skewness and heavy tails. In this paper, we introduce a package written in the R language called alphastable. The alphastable performs a variety of tasks including: 1- generating random numbers from univariate, truncated, and multivariate stable distributions. 2- computing the probability density function of univariate and multivariate elliptically contoured stable distributions, 3- computing the distribution function of univariate stable distributions, 4- estimating the parameters of univariate symmetric stable, univariate Cauchy, mixture of Cauchy, mixture of univariate symmetric stable, multivariate elliptically contoured stable, and multivariate strictly stable distributions. This package, as it will be shown, is very useful for modelling data in univariate and multivariate cases that arise in the fields of finance and economics.