Weighted Marshall–Olkin bivariate exponential distribution

Abstract

Recently, Gupta and Kundu [R.D. Gupta and D. Kundu, A new class of weighted exponential distributions, Statistics 43 (2009), pp. 621–634] have introduced a new class of weighted exponential (WE) distributions, and this can be used quite effectively to model lifetime data. In this paper, we introduce a new class of weighted Marshall–Olkin bivariate exponential distributions. This new singular distribution has univariate WE marginals. We study different properties of the proposed model. There are four parameters in this model and the maximum-likelihood estimators (MLEs) of the unknown parameters cannot be obtained in explicit forms. We need to solve a four-dimensional optimization problem to compute the MLEs. One data set has been analysed for illustrative purposes and finally we propose some generalization of the proposed model.

Keywords:

• joint probability density function
• conditional probability density function
• singular distribution
• maximum-likelihood estimators
• Fisher information matrix
• asymptotic distribution

Acknowledgements

The authors thank the two referees for their valuable suggestions which has helped them to improve the manuscript significantly. Part of this work has been supported by a grant from the Department of Science and Technology, Government of India.

Additional information

Notes on contributors

Debasis Kundu

Visiting professor at the King Saud University, Riyadh, Saudi Arabia.