Bayesian Inference Based on Robust Priors and MML Estimators: Part II, Skew Location-scale Distributions

Abstract

Motivated by the attractive features of robust priors and MML (modified maximum likelihood) estimators, we develop MML estimators and HPD (highest posterior density) estimators of the location and scale parameters of gamma distribution family which represents a wide class of skew distributions. We show that the proposed estimators have desirable properties. This paper is a sequel to an earlier paper (Bian and Tiku 1995) which deals with a family of symmetric distributions (Student t).

Keywords:

• AMS Classification
• 62F15

Keywords:

• Bayesian estimation
• gamma distribution
• highest posterior density estimator
• mode of poly-t density
• modified maximum likelihood estimators
• outliers

^†On leave from Memaster University, Canada

^†On leave from Memaster University, Canada

Notes

^†On leave from Memaster University, Canada