A new flexible bivariate discrete Rayleigh distribution generated by the Marshall-Olkin family

Abstract

In the statistical analysis of bivariate data, it is possible to have discrete observations instead of continuous data, as observed in many studies with survival data. In this study it is introduced a new bivariate discrete distribution derived from two Rayleigh distributions using a method proposed by Marshall and Olkin (1997) where an additional parameter is is introduced to a family of distributions related to the dependence structure of two discrete random variables $X_1$ and $X_2$ . The study results show that this new bivariate distribution has good statistical properties and a simple mathematical expression for its correlation coefficient. The usual classical and Bayesian estimators for the parameters of the new distribution are also presented. A simulation study is carried out in order to evaluate some frequentist properties of the proposed model. The usefulness of the proposed model is illustrated using a real medical dataset introduced in the literature in presence of censoring and covariates.