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

Abstract

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