This study proposes two types of bivariate Poisson extended exponential distributions: the basic bivariate Poisson extended exponential distribution and the Sarmanov-based bivariate Poisson extended exponential distribution. The two bivariate Poisson extended exponential distributions are then...

A random variable is difference-form decomposable (DFD) if it may be written as the difference of two i.i.d. random terms. We show that densities of such variables exhibit a remarkable degree of structure. Specifically, a DFD density can be neither approximately uniform, nor quasi convex, nor...

We characterize the distributions of posterior quantiles under a given prior. Unlike the distributions of posterior means, which are known to be mean-preserving contractions of the prior, the distributions of a posterior quantile coincide with a first-order stochastic dominance interval bounded...

In this study, we deal with the hypothesis testing problem of Poisson distributed data. The purpose of the test is to determine whether two collections of discrete data have the same Poisson rate. We review and compare several frequientist and Bayesian methods that deal with the problem, such as...

A new two-parameter model is proposed using the Kavya-Manoharan (KM) transformation family and Burr X (BX) distribution. The new model is called the Kavya-Manoharan-Burr X (KMBX) model. The statistical properties are obtained, involving the quantile (QU) function, moment (MOs), incomplete MOs,...