Censoring heavy-tail count distributions for parameter estimation with an application to stable distributions

TL;DR

This paper introduces a novel method using censoring and moment criteria for estimating parameters of count distributions, especially when traditional probability mass functions or moments are unavailable, with an application to stable distributions.

Contribution

It presents a new approach combining censoring and moment-based estimation for count distributions lacking closed-form pmfs or moments.

Findings

Effective parameter estimation for stable distributions.

Applicable to distributions with intractable pmfs.

Improves estimation accuracy in challenging cases.

Abstract

A new approach based on censoring and moment criterion is introduced for parameter estimation of count distributions when the probability generating function is available even though a closed form of the probability mass function and/or finite moments do not exist.