论文标题
使用现金统计数据，一种半分析解决方案，用于泊松数据最大似然拟合到线性模型
A semi-analytical solution to the maximum likelihood fit of Poisson data to a linear model using the Cash statistic
论文作者
论文摘要
[删节]现金统计量（也称为C Stat）通常用于分析低计数泊松数据，其中包括对自变量某些值的无效计数的数据。该统计数据的使用对于不能合并或重新添加的低计数数据特别有吸引力，而不会丢失分辨率。本文使用基于泊松的现金统计量为线性模型的最佳拟合参数提供了一种新的最大样本解决方案。本文介绍的解决方案提供了一种新的简单方法，用于测量基于泊松数据的任何基于泊松数据的线性模型的最佳拟合参数，包括带有零计数的数据。特别是，该方法强制执行以下要求：最佳拟合线性模型在整个自变量的支持过程中都是不负的。该方法以简单的算法进行了汇总，以适合任何大小的泊松计数数据，并以线性模型计数速率，这完全通过使用传统$χ^2 $统计量。
[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 $χ^2$ statistic.
