A consistent method of estimation for three-parameter generalized exponential distribution

Abstract

In this article, we provide a consistent method of estimation for the parameters of a three-parameter generalized exponential distribution which avoids the problem of unbounded likelihood function. The method is based on a maximum likelihood estimation of the shape parameter, which uses location and scale invariant statistic, originally proposed by Nagatsuka et al. (A consistent method of estimation for the three-parameter weibull distribution, Computational Statistics & Data Analysis 58:210–26). It has been shown that the estimators are unique and consistent for the entire range of the parameter space. We also present a Monte-Carlo simulation study along with the comparisons with some prominent estimation methods in terms of the bias and root mean square error. For the illustration purpose, the data analysis of a real lifetime data set has been reported.

KEYWORDS:

• Consistency
• Estimation
• Generalized exponential distribution
• Invariant statistic
• Likelihood
• Maximum likelihood estimation

Acknowledgments

The authors would like to thank the reviewers for their constructive comments which have helped to improve the paper significantly. We also would like to thank to High Performance Computing (HPC) systems at Computer Center, Indian Institute of Technology Kanpur.