# Bivariate Discrete Generalized Exponential Distribution

## TL;DR

This paper introduces a flexible bivariate discrete generalized exponential distribution, extending existing models, with properties analysis, an EM algorithm for parameter estimation, and application to real data.

## Contribution

It develops a new bivariate discrete distribution with a novel EM algorithm for efficient parameter estimation, expanding the modeling toolkit for discrete data.

## Key findings

- Distribution includes bivariate geometric as a special case
- Efficient EM algorithm for maximum likelihood estimation
- Successful application to real data set

## Abstract

In this paper we develop a bivariate discrete generalized exponential distribution, whose marginals are discrete generalized exponential distribution as proposed by Nekoukhou, Alamatsaz and Bidram ("Discrete generalized exponential distribution of a second type", Statistics, 47, 876 - 887, 2013). It is observed that the proposed bivariate distribution is a very flexible distribution and the bivariate geometric distribution can be obtained as a special case of this distribution. The proposed distribution can be seen as a natural discrete analogue of the bivariate generalized exponential distribution proposed by Kundu and Gupta ("Bivariate generalized exponential distribution", Journal of Multivariate Analysis, 100, 581 - 593, 2009). We study different properties of this distribution and explore its dependence structures. We propose a new EM algorithm to compute the maximum likelihood estimators of the unknown parameters which can be implemented very efficiently, and discuss some inferential issues also. The analysis of one data set has been performed to show the effectiveness of the proposed model. Finally we propose some open problems and conclude the paper.