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arXiv:2301.03087 (stat)
[Submitted on 8 Jan 2023]

Title:Bivariate binomial conditionals distributions with positive and negative correlations: A statistical study

Authors:Indranil Ghosh, Filipe Marques, Subrata Chakraborty
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Abstract:In this article, we discuss a bivariate distribution whose conditionals are univariate binomial distributions and the marginals are not binomial that exhibits negative correlation. Some useful structural properties of this distribution namely marginals, moments, generating functions, stochastic ordering are investigated. Simple proofs of negative correlation, marginal over-dispersion, distribution of sum and conditional given the sum are also derived. The distribution is shown to be a member of the multi-parameter exponential family and some natural but useful consequences are also outlined. The proposed distribution tends to a recently investigated conditional Poisson distribution studied by Ghosh et al. (2020). Finally, the distribution is fitted to two bivariate count data sets with an inherent negative correlation to illustrate its suitability.
Comments: 19 pages, 5 figures
Subjects: Methodology (stat.ME)
MSC classes: 60E, 62F
Cite as: arXiv:2301.03087 [stat.ME]
  (or arXiv:2301.03087v1 [stat.ME] for this version)
  https://doi.org/10.48550/arXiv.2301.03087

Submission history

From: Indranil Ghosh [view email]
[v1] Sun, 8 Jan 2023 18:53:28 UTC (5,951 KB)
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