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

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  • Royuela-del-Val, Javier
  • Simmross-Wattenberg, Federico
  • Alberola-López, Carlos

Abstract

α-stable distributions are a family of well-known probability distributions. However, the lack of closed analytical expressions hinders their application. Currently, several tools have been developed to numerically evaluate their density and distribution functions or to estimate their parameters, but available solutions either do not reach sufficient precision on their evaluations or are excessively slow for 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 α-stable parameter space. In this paper we present an R package and a C/C++ library with a MATLAB front-end that permit parallelized, fast and high precision evaluation of density, distribution and quantile functions, as well as random variable generation and parameter estimation of α-stable distributions in their whole parameter space. The described library can be easily integrated into third party developments.

Suggested Citation

  • Royuela-del-Val, Javier & Simmross-Wattenberg, Federico & Alberola-López, Carlos, 2017. "libstable: Fast, Parallel, and High-Precision Computation of α-Stable Distributions in R, C/C++, and MATLAB," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 78(i01).
    • Handle: RePEc:jss:jstsof:v:078:i01
    DOI: http://hdl.handle.net/10.18637/jss.v078.i01
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    References listed on IDEAS

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    1. Pavel Cizek & Wolfgang Karl Härdle & Rafal Weron, 2011. "Statistical Tools for Finance and Insurance (2nd edition)," HSC Books, Hugo Steinhaus Center, Wroclaw University of Technology, number hsbook1101, December.
    2. Weron, Rafal, 1996. "On the Chambers-Mallows-Stuck method for simulating skewed stable random variables," Statistics & Probability Letters, Elsevier, vol. 28(2), pages 165-171, June.
    3. Weron, Rafał, 2004. "Computationally intensive Value at Risk calculations," Papers 2004,32, Humboldt University of Berlin, Center for Applied Statistics and Economics (CASE).
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    Cited by:

    1. Viacheslav Saenko, 2020. "The Calculation of the Density and Distribution Functions of Strictly Stable Laws," Mathematics, MDPI, vol. 8(5), pages 1-38, May.

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