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

• Published in: Nuclear instruments & methods in physics research. Section A, Accelerators, spectrometers, detectors and associated equipment Accelerators, spectrometers, detectors and associated equipment, 2000-07, Vol.449 (1), p.383-395
• Main Authors: Almeida, F.M.L, Barbi, M, do Vale, M.A.B
• Format: Article
• Language: English
• ISSN: 0168-9002; 1872-9576
• DOI: 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.