Bayesian approach to parameter estimation of the generalized pareto distribution

• Published in: Test (Madrid, Spain) Vol. 12; no. 1; pp. 259 - 277
• Main Authors: de Zea Bermudez, P., Turkman, M. A. Amaral
• Format: Journal Article
• Language: English
• Published: Heidelberg Springer Nature B.V 01.06.2003
• Subjects: Parameter estimation; Studies
• ISSN: 1133-0686; 1863-8260
• DOI: 10.1007/BF02595822

Several methods have been used for estimating the parameters of the generalized Pareto distribution (GPD), namely maximum likelihood (ML), the method of moments (MOM) and the probability-weighted moments (PWM). It is known that for these estimators to exist, certain constraints have to be imposed on the range of the shape parameter,k, of the GPD. For instance, PWM and ML estimators only exist fork>-0.5 andk≤1, respectively. Moreover, and particularly for small sample sizes, the most efficient method to apply in any practical situation highly depends on a previous knowledge of the most likely values ofk. This clearly suggests the use of Bayesian techniques as a way of using prior information onk. In the present work, we address the issue of estimating the parameters of the GPD from a Bayesian point of view. The proposed approach is compared via a simulation study with ML, PWM and also with the elemental percentile method (EPM) which was developed by Castillo and Hadi (1997). The estimation procedure is then applied to two real data sets.[PUBLICATION ABSTRACT]