Statistics and Computing

, Volume 27, Issue 5, pp 1365–1382 | Cite as

Fast parallel \(\alpha \)-stable distribution function evaluation and parameter estimation using OpenCL in GPGPUs

  • Guillermo Julián-Moreno
  • Jorge E. López de Vergara
  • Iván González
  • Luis de Pedro
  • Javier Royuela-del-Val
  • Federico Simmross-Wattenberg


\(\alpha \)-Stable distributions are a family of probability distributions found to be suitable to model many complex processes and phenomena in several research fields, such as medicine, physics, finance and networking, among others. However, the lack of closed expressions makes their evaluation analytically intractable, and alternative approaches are computationally expensive. Existing numerical programs are not fast enough for certain applications and do not make use of the parallel power of general purpose graphic processing units. In this paper, we develop novel parallel algorithms for the probability density function and cumulative distribution function—including a parallel Gauss–Kronrod quadrature—, quantile function, random number generator and maximum likelihood estimation of \(\alpha \)-stable distributions using OpenCL, achieving significant speedups and precision in all cases. Thanks to the use of OpenCL, we also evaluate the results of our library with different GPU architectures.


Gaussian quadrature \(\alpha \)-Stable distribution Parallel algorithms Numerical algorithms OpenCL GPGPU 



This work was partially supported by the Spanish Ministry of Economy and Competitiveness under the projects PackTrack (TEC2012-33754), TRÁFICA (MINECO/FEDER TEC2015-69417-C2-1-R) and kt-WiSE-MR (TEC2014-57428R), and by the Universidad Autónoma de Madrid under the Project “Implementación de Modelos Computacionales Masivamente Paralelos” (CEMU-2013-14). The authors also thank the Spanish Junta de Castilla y León for grant VA136U13 and the Universidad de Valladolid–Banco de Santander Grant Program 2012.


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Guillermo Julián-Moreno
    • 1
  • Jorge E. López de Vergara
    • 1
  • Iván González
    • 1
  • Luis de Pedro
    • 1
  • Javier Royuela-del-Val
    • 2
  • Federico Simmross-Wattenberg
    • 2
  1. 1.Department of Electronics and Communication Technologies, Escuela Politécnica SuperiorUniversidad Autónoma de MadridMadridSpain
  2. 2.Image Processing Lab, E.T.S.I. TelecomunicaciónUniversidad de ValladolidValladolidSpain

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