A semi-analytical solution to the maximum-likelihood fit of Poisson data to a linear model using the Cash statistic. Issue 3 (17th February 2022)

• Record Type: Journal Article
• Authors: Bonamente, Massimiliano; Spence, David
• Is Part Of: Journal of applied statistics. Volume 49:Issue 3(2022)
• Page Start: 522
• Page End: 552
• Publication Date: 2022-02-17
• Subjects: Probability -- statistics -- maximum-likelihood methods -- cash statistic -- parameter estimation; 62F10 -- 62F30; Statistics -- Periodicals; 519.5
• DOI: 10.1080/02664763.2020.1820960
• Languages: English
• ISSNs: 0266-4763

Abstract

Abstract : The Cash statistic, also known as the 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 χ 2 statistic.