The Bivariate Modified Exponential Geometric Distribution: Model, Properties and Applications

Subject Areas : International Journal of Mathematical Modelling & Computations

Ahmadreza Zanboori ¹ , Karim Zare ² , Zahra Khodadadi ³

1 - Department of Statistics, Marvdasht Branch, Islamic Azad University, Marvdasht, Iran
2 - Department of Statistics, Marvdasht Branch, Islamic Azad University, Marvdasht, Iran
3 - Department of Statistics, Marvdasht Branch, Islamic Azad University, Marvdasht, Iran

Received: 2021-02-21 Accepted : 2021-05-22 Published : 2021-12-01

Keywords: Maximum Likelihood Estimation, Expectation‐Maximization algorithm, geometric minimum, bivariate model,

Abstract :

In this paper, we have introduced a five‐parameter bivariate model by taking a geometric minimum of the modified exponential distributions. It is observed that the maximum likelihood estimators of the unknown parameters cannot be obtained in closed form. We propose to use the EM algorithm to compute the maximum likelihood estimators of the unknown parameters. A number of simulation experiments have been performed to determine the effectiveness of the proposed EM algorithm. We analyze two datasets for illustrative purposes, and it is observed that the proposed models and the expectation‐maximization algorithm perform at a satisfactory level.