On a Class of Multivariate Negative Binomial Distributions.

Abstract

The negative binomial distribution arises in probability as the distribution of the waiting time to achieve a specified number of successes in a sequence of Bernoulli trials. In addition, it has been widely used in statistics as a model for a variety of data involving counts. Multivariate analogues of the negative binomial distribution are of interest as joint distributions of waiting times in Bernoulli trials and for modelling data involving pairs or m-tuples of possibly dependent counts. This paper considers m-variate distributions concentrated on Z(+) superscript m is identical to (Z(+)) superscript m where Z(+) = (0,1,2,...) and having negative binomial univariate marginal distributions. Such distributions will be called multivariate/m-variate negative binomial distributions. It is not hard to see that distributions of this form do not, for any fixed m, exhaust the class of all m-variate negative binomial distributions. Several types of counterexample can be constructed.

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Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1980
Accession Number
ADA095445

Entities

People

  • R. K. Milne

Organizations

  • University of North Carolina at Chapel Hill

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Communities of Interest

  • Energy and Power Technologies

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  • Analytic Functions
  • Binomials
  • Classification
  • Convergence
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  • Power Series
  • Probability
  • Probability Distributions
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Fields of Study

  • Mathematics

Readers

  • Statistical inference.