A Bayesian approach for estimating the parameters of an α-stable distribution

M. J. Karling, S. R.C. Lopes*, R. M. de Souza

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


The lack of closed representations for the density functions of the α-stable distributions, when considering Bayesian inference using Markov Chain Monte Carlo methods, has historically lead to the use of bivariate probability density functions [Buckle. Bayesian inference for stable distributions. J Am Stat Assoc. 1995;90:605–613] and Fast Fourier Transforms of their characteristic functions [Lombardi. Bayesian inference for α-stable distributions: a random walk MCMC approach. Comput Stat Data Anal. 2007;51(5):2688–2700]. We present a novel approach using a full power series representation for the probability density functions. The Bayesian estimation analysis is provided for two different parameterization systems for one-dimensional stable distributions. We provide an algorithm that makes use only of the power series representation. Three goodness-of-fit tests, based on the empirical distribution functions, and two types of loss functions with their respective decision rules to minimize the Bayesian risk, are included. A simulation study and two empirical applications are also presented.

Original languageEnglish (US)
Pages (from-to)1713-1748
Number of pages36
JournalJournal of Statistical Computation and Simulation
Issue number9
StatePublished - 2021


  • Bayesian techniques
  • goodness-of-fit tests
  • loss functions
  • parameterization systems
  • power series representations
  • simulations
  • α-stable distribution

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Statistics, Probability and Uncertainty
  • Applied Mathematics


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