BAYESIAN ESTIMATION FOR THE STABLE DISTRIBUTIONS IN THE PRESENCE OF COVARIATES WITH APPLICATIONS IN CLINICAL ISSUES

Abstract

In this paper we explore a Bayesian approach for stable distributions in presence of covari-ates. This class of distribution has great flexibility for fitting asymmetric and heavy-tailed empirical data. These models are commonly used for data sets in finance and insurance. In this paper we show that these distributions can also be used to fit clinical data. Since there is not an analytical form for the density probability function which implies in serious difficulties to obtain the maximum likelihood estimators for the parameters, we use Bayesian methods with data augmentation techniques to get the inferences of interest. In this study we also discuss the choice of different prior distributions for the parameters considering regression models for the location and scale parameters of the stable distribution. We use MCMC (Markov Chain Monte Carlo) algorithms to generate samples from the posterior distributions in order to evaluate the point and interval estimators. A great simplification is obtained using the OpenBugs software. Two real data examples illustrate the applicability of the proposed modeling approach.