Testing Goodness of Fit for the Poisson Assumption When Observations are Not Identically Distributed

Abstract

Tests for detecting negative binomial departures from a Poisson model are studied for the one-way-layout and regression-throughthe-origin cases. Approximations to the null and alternative distributions of these test statistics are presented. Locally optimal tests and tests suggested in the literature are compared in terms of asymptotic relative efficiency. Small sample comparisons are included.

Statistical Modeling of the Number of Deaths of Children in Bangladesh

“…Failure to reject the null hypothesis leads to the Poisson regression model. In this study we perform, Dean's P B [15] test for over-dispersion using a R packaged DCluster [18] that generates the test statistic P B = 13.5292 with p-value <0.000. Rejection of H 0 leads to the application of Negative Binomial type models.…”

Modeling heterogeneity and dependence for analysis of neuronal data

“…This likelihood ratio test should be asymptotically equivalent to the score tests proposed by Dean and Lawless [14] and Dean [15]. See also [16] for applications to three different cases.…”

“…This likelihood ratio test should be asymptotically equivalent to the score tests proposed by Dean and Lawless [14] and Dean [15]. See also [16] for applications to three different cases. It should be noted that standard 2 approximation to the null distribution of these test statistics does not work well in small or moderate sample size situations.…”

A Simulation Comparison of Several Procedures for Testing the Poisson Assumption

“…In Potthoff and Whittinghill (1966) a review of the ÷ 2 -test was made as well as a comparison of the two tests. Kim and Park (1992) extended the work of Collings and Margolin (1985) to derive locally optimal tests for the Poisson distribution against the negative binomial distribution for several other situations. Perry and Mead (1979) examined the power of the variance test when it is used to detect a spatial pattern.…”

“…This corresponds to a non-central ÷ 2 -distribution with the noncentrality parameter depending on the speci®c distribution. Various rami®cations of this test are given in Potthoff and Whittinghill (1966) and Collings and Margolin (1985). They both used this test in more complicated situations.…”