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Poisson Probability Distribution01:09

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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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A binomial distribution is a probability distribution for a procedure with a fixed number of trials, where each trial can have only two outcomes.
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Poisson's ratio is a material property that indicates their stress response. It explains the connection between the elongation or compression a material undergoes in the direction of an applied force and the contraction or expansion it experiences perpendicular to that force. When a slender bar is loaded axially, it stretches in the direction of the force and contracts laterally. Poisson's ratio is the negative ratio of this lateral contraction to the axial elongation. The negative sign...
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The accurate values of population parameters such as population proportion, population mean, and population standard deviation (or variance) are usually unknown. These are fixed values that can only be estimated from the data collected from the samples. The estimates of each of these parameters are sample proportion, the sample mean, and sample standard deviation (or variance). To obtain the values of these sample statistics, data are required that have particular distribution and central...
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A new bivariate Poisson distribution via conditional specification: properties and applications.

Indranil Ghosh1, Filipe Marques2, Subrata Chakraborty3

  • 1University of North Carolina, Wilmington, NC, USA.

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|June 16, 2022
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This study introduces a novel bivariate Poisson distribution exhibiting negative correlation, suitable for count data analysis. The distribution

Keywords:
Bivariate Poisson distributionEnglish premier league databivariate copulaconditional specificationcopula-based simulationnegative correlationseeds and plant grown data

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Area of Science:

  • Statistics
  • Probability Theory
  • Econometrics

Background:

  • Bivariate count data often exhibits complex dependency structures.
  • Existing bivariate Poisson models may not adequately capture negative correlations.

Purpose of the Study:

  • Introduce and investigate a novel bivariate Poisson distribution.
  • Address the challenge of modeling negatively correlated count data.
  • Explore structural properties and parameter estimation.

Main Methods:

  • Derivation of marginals, moments, and generating functions.
  • Investigation of stochastic ordering and over-dispersion.
  • Maximum likelihood estimation and copula-based simulations (Bivariate Normal, Farlie-Gumbel-Morgenstern).

Main Results:

  • The proposed distribution exhibits negative correlation and marginal over-dispersion.
  • Demonstrated suitability for modeling bivariate count data with negative dependence.
  • Parameter estimation via maximum likelihood proved effective.

Conclusions:

  • The novel bivariate Poisson distribution offers a valuable tool for analyzing negatively correlated count data.
  • The model's properties and estimation methods are well-defined.
  • Empirical fitting to real-world data confirms its practical applicability.