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

Massimiliano Bonamente and David Spence

Journal of Applied Statistics, 2022, vol. 49, issue 3, 522-552

Abstract: The Cash statistic, also known as the ${C} $C 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 $\chi ^2 $χ2 statistic.

Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:taf:japsta:v:49:y:2022:i:3:p:522-552

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DOI: 10.1080/02664763.2020.1820960

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