Discrete Stieltjes classes for log-Heine type distributions

TL;DR

This paper introduces a novel method for constructing Stieltjes classes for discrete distributions, expanding their application beyond continuous cases and providing examples for common discrete distributions.

Contribution

It presents a new approach to construct Stieltjes classes in the discrete setting, which was previously mainly considered for continuous distributions.

Findings

New discrete Stieltjes classes constructed for common distributions

Examples demonstrate the applicability of the method

Advances understanding of moment-indeterminate discrete distributions

Abstract

The Stieltjes classes play a significant role in the moment problem since they permit to expose an infinite family of probability distributions all having equal moments of all orders. Given a moment-indeterminate distribution, it may not be easy to indicate another distribution with the same moments. Mostly, the Stieltjes classes have been considered for absolutely continuous distributions. In this work, a new approach for constructing them in the discrete case is presented. Examples for some widely used discrete distributions are provided.