Libstable: Fast, Parallel and High-Precision Computation of -Stable Distributions in C/C++ and MATLAB

Abstract

-stable distributions are a wide family of probability distributions used in many elds where probabilistic approaches are taken. However, the lack of closed analytical expressions is a major drawback for their application. Currently, several tools have been developed to numerically evaluate their density and distribution functions or estimate their parameters, but available solutions either do not reach su cient precision on their evaluations or are too slow for several practical purposes. Moreover, they do not take full advantage of the parallel processing capabilities of current multi-core machines. Other solutions work only on a subset of the -stable parameter space. In this paper we present a C/C++ library and a MATLAB front-end that allows fully parallelized, fast and high precision evaluation of density, distribution and quantile functions (PDF, CDF and CDFð€€€1 respectively), random variable generation and parameter estimation of -stable distributions in their whole parameter space. The library provided can be easily integrated on third party developments.