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Poisson distribution

About: Poisson distribution is a research topic. Over the lifetime, 16314 publications have been published within this topic receiving 363895 citations.


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Book
01 Jan 1992
TL;DR: In this paper, the authors propose a family of Discrete Distributions, which includes Hypergeometric, Mixture, and Stopped-Sum Distributions (see Section 2.1).
Abstract: Preface. 1. Preliminary Information. 2. Families of Discrete Distributions. 3. Binomial Distributions. 4. Poisson Distributions. 5. Neggative Binomial Distributions. 6. Hypergeometric Distributions. 7. Logarithmic and Lagrangian Distributions. 8. Mixture Distributions. 9. Stopped-Sum Distributions. 10. Matching, Occupancy, Runs, and q-Series Distributions. 11. Parametric Regression Models and Miscellanea. Bibliography. Abbreviations. Index.

2,106 citations

Journal ArticleDOI
TL;DR: In this paper, a new SAS procedure, TRAJ, is proposed to fit semiparametric mixtures of censored normal, Poisson, zero-inflated Poisson and Bernoulli distributions to longitudinal data.
Abstract: This article introduces a new SAS procedure written by the authors that analyzes longitudinal data (developmental trajectories) by fitting a mixture model. The TRAJ procedure fits semiparametric (discrete) mixtures of censored normal, Poisson, zero-inflated Poisson, and Bernoulli distributions to longitudinal data. Applications to psychometric scale data, offense counts, and a dichotomous prevalence measure in violence research are illustrated. In addition, the use of the Bayesian information criterion to address the problem of model selection, including the estimation of the number of components in the mixture, is demonstrated.

2,085 citations

Journal ArticleDOI
TL;DR: Several classes of stochastic models for the origin times and magnitudes of earthquakes are discussed and the utility of seismic quiescence for the prediction of a major earthquake is investigated.
Abstract: This article discusses several classes of stochastic models for the origin times and magnitudes of earthquakes. The models are compared for a Japanese data set for the years 1885–1980 using likelihood methods. For the best model, a change of time scale is made to investigate the deviation of the data from the model. Conventional graphical methods associated with stationary Poisson processes can be used with the transformed time scale. For point processes, effective use of such residual analysis makes it possible to find features of the data set that are not captured in the model. Based on such analyses, the utility of seismic quiescence for the prediction of a major earthquake is investigated.

1,941 citations

Journal ArticleDOI
TL;DR: In this article, a general method for calculating the bias and variance of estimators for w(θ) based on galaxy-galaxy (DD), random-random (RR), and galaxy random (DR) pair counts is presented.
Abstract: We present a general method for calculating the bias and variance of estimators for w(θ) based on galaxy-galaxy (DD), random-random (RR), and galaxy-random (DR) pair counts and describe a procedure for quickly estimating these quantities given an arbitrary two-point correlation function and sampling geometry. These results, based conditionally upon the number counts, are accurate for both high and low number counts. We show explicit analytical results for the variances in the estimators DD/RR, DD/DR, which turn out to be considerably larger than the common wisdom Poisson estimate and report a small bias in DD/DR in addition to that due to the integral constraint. Further, we introduce and recommend an improved estimator (DD−2DR+RR)/RR, whose variance is nearly Poisson

1,874 citations

Journal ArticleDOI
TL;DR: In this article, the authors deal with specification, estimation and tests of single equation reduced form type equations in which the dependent variable takes only non-negative integer values, and provide a detailed application of the estimators and tests to a model of the number of doctor consultations.
Abstract: This paper deals with specification, estimation and tests of single equation reduced form type equations in which the dependent variable takes only non-negative integer values. Beginning with Poisson and compound Poisson models, which involve strong assumptions, a variety of possible stochastic models and their implications are discussed. A number of estimators and their properties are considered in the light of uncertainty about the data generation process. The paper also considers the role of tests in sequential revision of the model specification beginr ing with the Poisson case and provides a detailed application of the estimators and tests to a model of the number of doctor consultations.

1,838 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20251
20244
2023890
20221,909
2021798
2020777