Statistics of weighted Poisson events and its applications

TL;DR

This paper explores the statistical properties of weighted Poisson events, introduces an approximation method for the compound Poisson distribution, and presents a bootstrap technique for confidence interval estimation in relevant physical applications.

Contribution

It introduces a scaled Poisson distribution approximation for the compound Poisson distribution and a bootstrap method for confidence limits, enhancing analysis of weighted Poisson data.

Findings

SPD outperforms normal approximation in parameter estimation

Bootstrap technique enables confidence interval derivation for CPD

Application to nuclear and particle physics data

Abstract

The statistics of the sum of random weights where the number of weights is Poisson distributed has important applications in nuclear physics, particle physics and astrophysics. Events are frequently weighted according to their acceptance or relevance to a certain type of reaction. The sum is described by the compound Poisson distribution (CPD) which is shortly reviewed. It is shown that the CPD can be approximated by a scaled Poisson distribution (SPD). The SPD is applied to parameter estimation in situations where the data are distorted by resolution effects. It performs considerably better than the normal approximation that is usually used. A special Poisson bootstrap technique is presented which permits to derive confidence limits for observations following the CPD.