A Generalization of the Poisson Distribution

Demographic stochasticity can have large effects on the dynamics of small populations as well as on the persistence of rare genotypes and lineages. Survival is sensibly modeled as a binomial process, but annual reproductive success (ARS) is more complex and general models for demographic stochasticity do not exist. Here we introduce a stochastic model framework for ARS and illustrate some of its properties. We model a sequence of stochastic events: nest completion, the number of eggs or neonates produced, nest predation, and the survival of individual offspring to independence. We also allow multiple nesting attempts within a breeding season. Most of these components can be described by Bernoulli or binomial processes; the exception is the distribution of offspring number. Using clutch and litter size distributions from 53 vertebrate species, we demonstrate that among-individual variability in offspring number can usually be described by the generalized Poisson distribution. Our model framework allows the demographic variance to be calculated from underlying biological processes and can easily be linked to models of environmental stochasticity or selection because of its parametric structure. In addition, it reveals that the distributions of ARS are often multimodal and skewed, with implications for extinction risk and evolution in small populations.

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“…A stochastic process very much like this is described by the "generalized Poisson distribution" (Consul and Jain 1973;Consul 1989).…”

Section: Clutch Size Distributionsmentioning

confidence: 99%

A Stochastic Model for Annual Reproductive Success

Kendall

Wittmann

2010

The American Naturalist

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“…Meanwhile, the values of p and n are not constant due to the diversity of attractive abilities of papers and authors. Hence it is reasonable to think the number of citations received by lowly cited authors and papers are drawn from generalized Poisson distributions, which relax the restrictions of Poisson distribution by allowing the probability of occurrence of a single event to affect by previous occurrences [35]. For highly cited papers (with large np) and authors, the numbers of citations are large enough to suppose the "yes/no" decisions are independent.…”

Section: Modeling the Distributions Of Specific Indexes Per Authormentioning

confidence: 99%

Modeling the coevolution between citations and coauthorship of scientific papers

Xie¹,

Xie²,

Li³

et al. 2017

Scientometrics

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Collaborations and citations within scientific research grow simultaneously and interact dynamically.Modelling the coevolution between them helps to study many phenomena that can be approached only through combining citation and coauthorship data. A geometric graph for the coevolution is proposed, the mechanism of which synthetically expresses the interactive impacts of authors and papers in a geo-

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“…Consider the GP distribution (Chandra, Roy, & Ghosh, 2013;Consul & Jain, 1973;Hubert, Lauretto, & Stern, 2009;Lerner, Lone, & Rao, 1997;Srivastava & Chen, 2010;Tuenter, 2006) (following the notation of Consul & Jain, 1973) of a random variable X with the following probability function…”

Section: Generalised Poisson Difference Distributionmentioning

confidence: 99%

Bayesian Modelling of Integer Data Using the Generalised Poisson Difference Distribution

Shahtahmassebi¹,

Moyeed²

2014

IJSP

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Integer-valued random variables arising from the difference of two discrete variables can be seen frequently in various applications. In this paper, we obtain the distribution and derive the properties of the difference of two generalised Poisson variables with unequal parameters. This distribution is adopted to model a set of ultra high frequency (UHF) data relating to FTSE100 index futures using covariates. The unique characteristics of UHF data have introduced new theoretical and computational challenges to both statistical and financial studies. Such data consist of discrete-valued observations and unequally spaced time intervals. We also extend the model to its zero inflated version in order to capture the excess of zeros in the given data set. The analysis is carried out in a Bayesian framework using Markov Chain Monte Carlo methods. Various model diagnostics and model comparisons were undertaken which showed that index changes were explained well by the fitted model.

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A Generalization of the Poisson Distribution

Cited by 448 publications

References 7 publications

A Stochastic Model for Annual Reproductive Success

A Stochastic Model for Annual Reproductive Success

Modeling the coevolution between citations and coauthorship of scientific papers

Bayesian Modelling of Integer Data Using the Generalised Poisson Difference Distribution

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