New technique for parameter estimation and improved fits to experimental data for a set of compound Poisson distributions

TL;DR

This paper introduces a novel parameter estimation technique for compound Poisson distributions using the power spectrum, resulting in significantly improved fits to experimental data compared to traditional methods.

Contribution

A new method employing the power spectrum for better parameter estimation of compound Poisson distributions is proposed and demonstrated on published datasets.

Findings

Better fits achieved than previous methods

Significant improvements in some cases

Enhances tools for parameter estimation

Abstract

Compound Poisson distributions have been employed by many authors to fit experimental data, typically via the method of moments or maximum likelihood estimation. We propose a new technique and apply it to several sets of published data. It yields better fits than those obtained by the original authors for a set of widely employed compound Poisson distributions (in some cases, significantly better). The technique employs the power spectrum (the absolute square of the characteristic function). The new idea is suggested as a useful addition to the tools for parameter estimation of compound Poisson distributions.