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A semi-analytical solution to the maximum-likelihood fit of Poisson data to a linear model using the Cash statistic.
- Source :
-
Journal of Applied Statistics . Mar 2022, Vol. 49 Issue 3, p522-552. 31p. 1 Chart, 8 Graphs. - Publication Year :
- 2022
-
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. [ABSTRACT FROM AUTHOR]
- Subjects :
- *DATA modeling
*INDEPENDENT variables
*ANALYTICAL solutions
*PARAMETER estimation
Subjects
Details
- Language :
- English
- ISSN :
- 02664763
- Volume :
- 49
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Journal of Applied Statistics
- Publication Type :
- Academic Journal
- Accession number :
- 155283711
- Full Text :
- https://doi.org/10.1080/02664763.2020.1820960