Details

Autor(en) / Beteiligte

• Bonamente, Massimiliano
• Spence, David

Titel

A semi-analytical solution to the maximum-likelihood fit of Poisson data to a linear model using the Cash statistic

Ist Teil von

• Journal of applied statistics, 2022-02, Vol.49 (3), p.522-552

Ort / Verlag

England: Taylor & Francis

Erscheinungsjahr

2022

Link zum Volltext

Quelle

EBSCOhost Business Source Ultimate

Beschreibungen/Notizen

• The Cash statistic, also known as the statistic, is commonly used for the analysis of low-count Poisson data, including data with null counts for certain values of the independent variable. The use of this statistic is especially attractive for low-count data that cannot be combined, or re-binned, without loss of resolution. This paper presents a new maximum-likelihood solution for the best-fit parameters of a linear model using the Poisson-based Cash statistic. The solution presented in this paper provides a new and simple method to measure the best-fit parameters of a linear model for any Poisson-based data, including data with null counts. In particular, the method enforces the requirement that the best-fit linear model be non-negative throughout the support of the independent variable. The method is summarized in a simple algorithm to fit Poisson counting data of any size and counting rate with a linear model, by-passing entirely the use of the traditional statistic.