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Maximum-likelihood fits to histograms for improved parameter estimation



Joseph W. Fowler


Straightforward methods for adapting the familiar χ2 statistic to histograms of discrete events and other Poisson distributed data generally yield biased estimates of the parameters of a model. The bias can be important even when the total number of events is large. For the case of estimating a microcalorimeter's energy resolution at 6 keV from the observed shape of the Mn K α fluorescence spectrum, a poor choice of χ2 can lead to biases of at least 10% in the estimated resolution when up to thousands of photons are observed. The best remedy is a Poisson maximum-likelihood fit, through a simple modification of the standard Levenberg-Marquardt algorithm for χ2 minimization. Where the modification is not possible, another approach allows iterative approximation of the maximum-likelihood fit.
Journal of Low Temperature Physics


Histogram fitting, energy resolution, maximum likelihood


Fowler, J. (2014), Maximum-likelihood fits to histograms for improved parameter estimation, Journal of Low Temperature Physics, [online], (Accessed May 20, 2024)


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Created February 7, 2014, Updated November 10, 2018