[ABRIDGED] The Cash statistic, also known as the C stat, 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 $\chi^2$ statistic.
翻译:[ABRIDGED] 现金统计(又称Cstat) 通常用于分析低计 Poisson 数据,包括独立变量某些值的无效计数数据。使用这一统计对低计数数据特别有吸引力,这些数据在不丧失分辨率的情况下是无法合并或重新组合的。本文为使用Poisson 基现金统计的线性模型的最佳适用参数提供了一个新的最大相似性解决方案。本文提出的解决方案为测量任何 Poisson 基数据线性模型的最佳参数提供了一个新的简单方法,包括无效计数数据。特别是,该方法强制要求最合适的线性模型在支持独立变量的整个过程中是非负性的。该方法在简单算法中作了总结,将任何大小和计价率的Poisson数据与线性模型相匹配,并完全通过使用传统的 $\chi2$统计。