The Poisson distribution has a large number of applications and is often used as a model in both a practical and a theoretical setting. As a result, various goodness-of-fit tests have been developed for this distribution. In this paper, we compare the finite sample power performance of ten of these tests against a wide range of alternative distributions for various sample sizes. The alternatives considered include, seemingly for the first time, weighted Poisson distributions. A number of additional tests are of historical importance although their power performance is not competitive against the remaining tests. These tests are discussed, but their powers are not included in the numerical analysis. The Monte Carlo study presented below indicates that the test with the best overall power performance is the test of Meintanis and Nikitin (2008), followed closely by the test of Rayner and Best (1990) (originally studied in Fisher, 1950).
Within statistical process control (SPC), normality is often assumed as the underlying probabilistic generator where the process variance is assumed equal for all rational subgroups. The parameters of the underlying process are usually assumed to be known—if this is not the case, some challenges arise in the estimation of unknown parameters in the SPC environment especially in the case of few observations. This paper proposes a bivariate beta type distribution to guide the user in the detection of a permanent upward or downward step shift in the process’ variance that does not directly rely on parameter estimates, and as such presents itself as an attractive and intuitive approach for not only potentially identifying the magnitude of the shift, but also the position in time where this shift is most likely to occur. Certain statistical properties of this distribution are derived and simulation illustrates the theoretical results. In particular, some insights are gained by comparing the newly proposed model’s performance with an existing approach. A multivariate extension is described, and useful relationships between the derived model and other bivariate beta distributions are also included.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.