A goodness of fit test for the Poisson distribution based on the empirical generating function

L. Baringhaus and N. Henze

Statistics & Probability Letters, 1992, vol. 13, issue 4, 269-274

Abstract: The generating function g(t) of the Poisson distribution with parameter [lambda] is the only generating function satisfying the differential equation g'(t) = [lambda]g(t). Denoting by gn(t) the empirical generating function of a random sample X1,..., Xn of size n drawn from a distribution concentrated on the nonnegative integers, we propose Tn = n[integral operator]01[n(t)- g'n(t)]2 dt as a goodness of fit statistic for the composite hypothesis that the distribution of Xi is Poisson. Using a parametric bootstrap to have a critical value, and estimating this in turn by Monte Carlo the resulting test is shown to be consistent against alternative distributions with finite expectation.

Keywords: Poisson; distribution; goodness; of; fit; empirical; generating; function; bootstrapping; Monte; Carlo; samples (search for similar items in EconPapers)
Date: 1992
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Citations: View citations in EconPapers (17)

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