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

We obtain an approximate Gaussian distribution from a Poisson distribution after doing a change of variable. A new chi-square function is obtained whi ch can be used for parameter estimations and goodness-of-fit testing when a djusting curves to histograms. Since, the new distribution is approximately Gaussian we can use if even when the bin contents are small. The correspon ding chi-square function can be used for curve fitting. This chi-square fun ction is simple to implement and presents a fast convergence of the paramet ers to the correct value, especially for the parameters associated with the width of the fitted curve. We present a Monte Carlo comparative study of t he fitting method introduced here and two other methods for three types of curves: Gaussian, Breit-Wigner and Moyal, when each bin content obeys a Poi sson distribution. It is also shown that the new method and the other two c onverge to the same result when the number of events increases. (C) 2000 El sevier Science B.V. All rights reserved.