TY - JOUR
T1 - A form of bivariate binomial conditionals distributions
AU - Ghosh, Indranil
AU - Marques, Filipe
AU - Chakraborty, Subrata
N1 - info:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDB%2F00297%2F2020/PT#
info:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDP%2F00297%2F2020/PT#
Publisher Copyright:
© 2024 Taylor & Francis Group, LLC.
PY - 2024
Y1 - 2024
N2 - Abstract.: In this article, we discuss a bivariate distribution whose conditionals are univariate binomial distributions, but the marginals are not binomial that exhibits both positive and negative correlation. Some useful structural properties of this distribution namely marginals, moments, generating functions, stochastic ordering are investigated. Simple proofs of both positive and negative correlation, marginal over-dispersion, the distribution of the maximum and minimum order statistics for a random sample of size 2 are also derived. The distribution is shown to be a member of the multi-parameter exponential family, and some natural and useful consequences are also outlined. The proposed distribution reduces to another bivariate discrete distribution, namely the bivariate Poisson conditionals recently studied by Ghosh, Marques, and Chakraborty (2021) under certain parametric conditions. Finally, the distribution is fitted to two bivariate count data sets having positive and negative correlation separately to illustrate its’ suitability.
AB - Abstract.: In this article, we discuss a bivariate distribution whose conditionals are univariate binomial distributions, but the marginals are not binomial that exhibits both positive and negative correlation. Some useful structural properties of this distribution namely marginals, moments, generating functions, stochastic ordering are investigated. Simple proofs of both positive and negative correlation, marginal over-dispersion, the distribution of the maximum and minimum order statistics for a random sample of size 2 are also derived. The distribution is shown to be a member of the multi-parameter exponential family, and some natural and useful consequences are also outlined. The proposed distribution reduces to another bivariate discrete distribution, namely the bivariate Poisson conditionals recently studied by Ghosh, Marques, and Chakraborty (2021) under certain parametric conditions. Finally, the distribution is fitted to two bivariate count data sets having positive and negative correlation separately to illustrate its’ suitability.
KW - Bivariate binomial distribution
KW - conditional failure rate
KW - conditional specification
KW - limiting distribution
KW - negative and positive correlation
UR - http://www.scopus.com/inward/record.url?scp=85186186329&partnerID=8YFLogxK
U2 - 10.1080/03610926.2024.2315294
DO - 10.1080/03610926.2024.2315294
M3 - Article
AN - SCOPUS:85186186329
SN - 0361-0926
JO - Communications in Statistics - Theory and Methods
JF - Communications in Statistics - Theory and Methods
ER -