Asymptotic tail properties of the distributions in the class of dispersion models

TL;DR

This paper investigates the asymptotic tail behavior of distributions within the dispersion models class, extending previous results by analyzing small dispersion limits and saddlepoint approximations.

Contribution

It provides new insights into the tail properties of dispersion models, broadening understanding of their asymptotic behavior under small dispersion conditions.

Findings

Extended tail behavior analysis for dispersion models

Generalized results beyond previous specific cases

Applicable to a wide range of known distributions

Abstract

The class of dispersion models introduced by J{\o}rgensen (1997b) covers many known distributions such as the normal, Student t, gamma, inverse Gaussian, hyperbola, von-Mises, among others. We study the small dispersion asymptotic (J{\o}rgensen, 1987b) behavior of the probability density functions of dispersion models which satisfy the uniformly convergent saddlepoint approximation. Our results extend those obtained by Finner et al. (2008).