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

M. J. Karling; S. R.C. Lopes; R. M. de Souza

doi:10.1080/00949655.2020.1865958

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

Computer, Electrical and Mathematical Sciences and Engineering

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

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)
Pages (from-to)	1713-1748
Number of pages	36
Journal	Journal of Statistical Computation and Simulation
Volume	91
Issue number	9
DOIs	https://doi.org/10.1080/00949655.2020.1865958
State	Published - 2021

Bibliographical note

Funding Information:
M.J. Karling was supported by CAPES-Brazil and CNPq-Brazil. S.R.C. Lopes' re- search was partially supported by CNPq-Brazil.

Funding Information:
M.J. Karling was supported by CAPES-Brazil and Conselho Nacional de Desenvolvimento Cient?fico e Tecnol?gico (CNPq)-Brazil. S.R.C. Lopes' research was partially supported by CNPq-Brazil [170168/2018-2,303453/2018-4]. M.J. Karling was supported by CAPES-Brazil and CNPq-Brazil. S.R.C. Lopes' research was partially supported by CNPq-Brazil. The authors would like to thank the associated editor and two anonymous referees who kindly reviewed the earlier versions of this work, providing valuable suggestions and comments.

Publisher Copyright:
© 2020 Informa UK Limited, trading as Taylor & Francis Group.

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

Access to Document

10.1080/00949655.2020.1865958

Cite this

@article{d201b9c8ff844ab5ab3f7f86541c6699,

title = "A Bayesian approach for estimating the parameters of an α-stable distribution",

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.",

keywords = "Bayesian techniques, goodness-of-fit tests, loss functions, parameterization systems, power series representations, simulations, α-stable distribution",

author = "Karling, {M. J.} and Lopes, {S. R.C.} and {de Souza}, {R. M.}",

note = "Funding Information: M.J. Karling was supported by CAPES-Brazil and CNPq-Brazil. S.R.C. Lopes' re- search was partially supported by CNPq-Brazil. Funding Information: M.J. Karling was supported by CAPES-Brazil and Conselho Nacional de Desenvolvimento Cient?fico e Tecnol?gico (CNPq)-Brazil. S.R.C. Lopes' research was partially supported by CNPq-Brazil [170168/2018-2,303453/2018-4]. M.J. Karling was supported by CAPES-Brazil and CNPq-Brazil. S.R.C. Lopes' research was partially supported by CNPq-Brazil. The authors would like to thank the associated editor and two anonymous referees who kindly reviewed the earlier versions of this work, providing valuable suggestions and comments. Publisher Copyright: {\textcopyright} 2020 Informa UK Limited, trading as Taylor & Francis Group.",

year = "2021",

doi = "10.1080/00949655.2020.1865958",

language = "English (US)",

volume = "91",

pages = "1713--1748",

journal = "Journal of Statistical Computation and Simulation",

issn = "0094-9655",

publisher = "Taylor and Francis Ltd.",

number = "9",

}

TY - JOUR

T1 - A Bayesian approach for estimating the parameters of an α-stable distribution

AU - Karling, M. J.

AU - Lopes, S. R.C.

AU - de Souza, R. M.

N1 - Funding Information: M.J. Karling was supported by CAPES-Brazil and CNPq-Brazil. S.R.C. Lopes' re- search was partially supported by CNPq-Brazil. Funding Information: M.J. Karling was supported by CAPES-Brazil and Conselho Nacional de Desenvolvimento Cient?fico e Tecnol?gico (CNPq)-Brazil. S.R.C. Lopes' research was partially supported by CNPq-Brazil [170168/2018-2,303453/2018-4]. M.J. Karling was supported by CAPES-Brazil and CNPq-Brazil. S.R.C. Lopes' research was partially supported by CNPq-Brazil. The authors would like to thank the associated editor and two anonymous referees who kindly reviewed the earlier versions of this work, providing valuable suggestions and comments. Publisher Copyright: © 2020 Informa UK Limited, trading as Taylor & Francis Group.

PY - 2021

Y1 - 2021

N2 - 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.

AB - 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.

KW - Bayesian techniques

KW - goodness-of-fit tests

KW - loss functions

KW - parameterization systems

KW - power series representations

KW - simulations

KW - α-stable distribution

UR - http://www.scopus.com/inward/record.url?scp=85098580120&partnerID=8YFLogxK

U2 - 10.1080/00949655.2020.1865958

DO - 10.1080/00949655.2020.1865958

M3 - Article

AN - SCOPUS:85098580120

SN - 0094-9655

VL - 91

SP - 1713

EP - 1748

JO - Journal of Statistical Computation and Simulation

JF - Journal of Statistical Computation and Simulation

IS - 9

ER -

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

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this