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.
Original language | English (US) |
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Pages (from-to) | 1713-1748 |
Number of pages | 36 |
Journal | Journal of Statistical Computation and Simulation |
Volume | 91 |
Issue number | 9 |
DOIs | |
State | Published - 2021 |
Keywords
- 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