On new tests for the Poisson distribution based on empirical weight functions
Year: 2025
Type: article
Abstract: We propose new goodness-of-fit tests for the Poisson distribution. The testing procedure entails fitting a weighted Poisson distribution, which has the Poisson as a special case, to observed data. Based on sample data, we calculate an empirical weight function which is compared to its theoretical counterpart under the Poisson assumption. Weighted Lp distances between these empirical and theoretical functions are proposed as test statistics and closed form expressions are derived for L1, L2 and L∞ distances. A Monte Carlo study is included in which the newly proposed tests are shown to be powerful when compared to existing tests, especially in the case of overdispersed alternatives. We demonstrate the use of the tests with two practical examples. Keywords: Goodness-of-fit, Poisson distribution, Weighted Lp distances
Authors: WC Kirui, E Bothma, M Smuts, A Steyn, IJH Visagie
Institution: North-West University
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4414616212