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A Poisson probability distribution is a discrete probability distribution. It gives the probability of a number of events occurring in a fixed interval of time or space if these events happen at a known average rate and independently of the time since the last event. For example, a book editor might be interested in the number of words spelled incorrectly in a particular book. It might be that, on average, there are five words spelled incorrectly in 100 pages. The interval is 100 pages.
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Statistical inference for distributions with one Poisson conditional.

Barry C Arnold1, B G Manjunath2

  • 1Department of Statistics, University of California, Riverside, CA, USA.

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Summary
This summary is machine-generated.

This study introduces Pseudo-Poisson distributions, a flexible bivariate model for dependent data. These models feature one Poisson marginal distribution and Poisson conditionals, addressing limitations of independent Poisson variables.

Keywords:
Pseudo-Poissonindex of dispersionlikelihood ratio testmarginal and conditional distributionsmaximum-likelihood estimators

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Area of Science:

  • Statistics
  • Probability Theory
  • Statistical Modeling

Background:

  • Classical bivariate normal distributions exhibit normal marginals and conditionals.
  • Independent Poisson variables are the only case with both Poisson marginals and conditionals.
  • Existing models lack flexibility for dependent Poisson components.

Purpose of the Study:

  • Introduce and define Pseudo-Poisson distributions.
  • Explore the distributional characteristics of these novel models.
  • Investigate inferential methods for Pseudo-Poisson distributions.

Main Methods:

  • Focus on bivariate distributions with one Poisson marginal and Poisson conditionals.
  • Develop theoretical properties of Pseudo-Poisson distributions.
  • Apply the model to real-world over-dispersed data.

Main Results:

  • Pseudo-Poisson distributions offer a flexible dependent bivariate model.
  • The study details the distributional features and inferential aspects.
  • Demonstrated applicability to over-dispersed datasets.

Conclusions:

  • Pseudo-Poisson distributions provide a valuable tool for analyzing dependent count data.
  • The model extends beyond independent Poisson variables.
  • Suitable for applications involving over-dispersed count data.