The Poisson distribution is a popular distribution used to describe count information, from which control charts involving count data have been established. Several works recognize the need for a generalized control chart to allow for data over-dispersion; however, analogous arguments can also be made to account for potential underdispersion. The Conway–Maxwell–Poisson (COM-Poisson) distributio...

C-control chart assumes that process nonconformities follow a Poisson distribution. In actuality, however, this Poisson distribution does not always occur. A process control for semiconductor based on a Poisson distribution always underestimates the true average amount of nonconformities and the process variance. Quality is described more accurately if a compound Poisson process is used for pro...

C-control chart assumes that process nonconformities follow a Poisson distribution. In actuality, however, this Poisson distribution does not always occur. A process control for semiconductor based on a Poisson distribution always underestimates the true average amount of nonconformities and the process variance. Quality is described more accurately if a compound Poisson process is used for pro...

We examined faecal egg count reduction tests (FECRTs) conducted with hookworm-infected humans in Ghana in 2007 (study 1) and 2010 (study 2) in order to explore aspects of the test analysis. Some subjects showed increased FEC following drug treatment. This occurred mostly in <150 epg pre-treatment FEC subjects. We sought a means to remove 'erroneous' negative drug efficacy cases from the FECRT a...

In this paper a new generalization of the hyper-Poisson distribution is proposed using the Mittag-Leffler function. The hyper-Poisson, displaced Poisson, Poisson and geometric distributions among others are seen as particular cases. This Mittag-Leffler function distribution (MLFD) belongs to the generalized hypergeometric and generalized power series families and also arises as weighted Poisson...

A useful discrete distribution (the Conway–Maxwell–Poisson distribution) is revived and its statistical and probabilistic properties are introduced and explored. This distribution is a two-parameter extension of the Poisson distribution that generalizes some well-known discrete distributions (Poisson, Bernoulli and geometric). It also leads to the generalization of distributions derived from th...

It might be that the two fundamental distributions in probability are the normal and the Poisson. Making these into processes with independent incre-Nevertheless, graduate training in probability tends to ignore Poisson processes and none of the almost 200 entries in the Probability and Statistics category of the 1991 Mathematics Subject Classification explicitly mentions Poisson, either. Brown...

The excursion{set, Press{Schechter mass spectrum for a Poisson distribution of identical particles is derived. For the special case of an initially Poisson distribution the spatial distribution of the Press{Schechter clumps is shown to be Poisson. Thus, the distribution function of particle counts in randomly placed cells is easily obtained from the Press{Schechter multiplicity function. This P...

Traditional techniques for calculating control limits for processes with discrete responses are based on the Poisson distribution. However, for many processes, the assumption of a Poisson distribution is violated. In such cases, use of traditional Poisson control limits may result in an inflated risk of Type I error. The negative binomial distribution is a natural extension of the Poisson distr...