The Kendal- Ressel Exponential Dispersion Model: Some Statistical Aspects and Estimation

Abstract

In this paper we revisit the NEF class of distributions generated by the Kendall-Ressel density. We study some of the statistical properties of this class (KR-NEF), as well as those of an associated class of Exponential Dispersion Model (KR-EDM). In particular, we discuss some of the immediate properties of these distributions, especially under the so called mean re-parameterization. The moments and other cumulants of these distributions are thoroughly presented as well as expressions for the measures of their skewness and kurtosis. Estimation procedures under the mean parameterization are also discussed where the maximum likelihood, second order minimax and a Bayes estimators are presented and illustrated.