A proposal for a different chi-square function for Poisson distributions

Details A proposal for a different chi-square function for Poisson distributions A proposal for a different chi-square function for Poisson distributions

1999-11-29

arxiv.org/abs/hep-ex/9911042v2

Nucl.Instrum.Meth. A449 (2000) 383-395

Physics

High Energy Physics

High Energy Physics - Experiment

27 pages, 13 figures

Scientific paper

10.1016/S0168-9002(99)01466-7

We obtain an approximate Gaussian distribution from a Poisson distribution after doing a change of variable. A new chi-square function is obtained which can be used for parameter estimations and goodness-of-fit testing when adjusting curves to histograms. Since the new distribution is approximately Gaussian we can use it even when the bin contents are small. The corresponding chi-square function can be used for curve fitting. This chi-square function is simple to implement and presents a fast convergence of the parameters to the correct value, especially for the parameters associated with the width of the fitted curve. We present a Monte Carlo comparative study of the fitting method introduced here and two other methods for three types of curves: Gaussian, Breit-Wigner and Moyal, when each bin content obeys a Poisson distribution. It is also shown that the new method and the other two converge to the same result when the number of events increases

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