A semi-analytical solution to the maximum-likelihood fit of Poisson data to a linear model using the Cash statistic |
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Authors: | Massimiliano Bonamente David Spence |
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Institution: | Department of Physics and Astronomy, University of Alabama in Huntsville, Huntsville, AL, USA |
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Abstract: | 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. |
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Keywords: | Probability statistics maximum-likelihood methods cash statistic parameter estimation |
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