A Bayesian approach for estimating the parameters of an α-stable distribution. Issue 9 (13th June 2021)

• Record Type: Journal Article
• Authors: Karling, M. J.; Lopes, S. R. C.; de Souza, R. M.
• Is Part Of: Journal of statistical computation and simulation. Volume 91:Issue 9(2021)
• Page Start: 1713
• Page End: 1748
• Publication Date: 2021-06-13
• Subjects: α-stable distribution -- parameterization systems -- Bayesian techniques -- power series representations -- goodness-of-fit tests -- loss functions -- simulations; 62C10 -- 60G52 -- 62P05 -- 62P10; Mathematical statistics -- Data processing -- Periodicals; Digital computer simulation -- Periodicals; 519.5028505
• DOI: 10.1080/00949655.2020.1865958
• Languages: English
• ISSNs: 0094-9655

Abstract

Abstract : 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.