Abstract
This article proposes a novel class of bivariate distributions that are completely defined by stating their conditionals as Poisson exponential distributions. Numerous statistical properties of this distribution are also examined here, including the conditional probability mass function (PMF) and moments of the new class. The techniques of maximum likelihood and pseudolikelihood are used to estimate the model parameters. Additionally, the effectiveness of the bivariate Poisson exponential conditional (BPEC) distribution is compared to that of the bivariate Poisson conditional (BPC), the bivariate Poisson (BP), the bivariate Poisson–Lindley (BPL), and the bivariate negative binomial (BNB) distributions using a real-world dataset. The findings of Akaike information criterion (AIC) and Bayesian information criterion (BIC) reveal that the BPEC distribution performs better than the other distributions considered in this study. As a result, the authors claim that this distribution may be used to fit dependent and overspread count data.
Highlights
In many areas of application, it is appropriate to study discrete bivariate variables
A new class of bivariate distribution has been proposed which is fully characterized by specifying its conditionals as Poisson exponential distribution
In accordance with (10) and (11), the class of discrete bivariate distribution with Poisson exponential conditionals is that given by (4), which describes the complete class of the bivariate Poisson exponential conditional (BPEC) distribution that has the three parameters θ1, θ2, and θ3 ∈ R, where θ3 0 corresponds to independence between J and K
Summary
In many areas of application, it is appropriate to study discrete bivariate variables. E use of this type of distribution in risk analysis and economics is relatively new; some applications were done by Sarabia et al [30, 31]. In this paper, another class of bivariate model for Poisson exponential conditionals will be considered. A new class of bivariate distribution has been proposed which is fully characterized by specifying its conditionals as Poisson exponential distribution. The performance of this distribution is compared with other distributions considering a real-life dataset
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