Estimating the Parameters of a Generalized Exponential Distribution

Abstract

A three-parameter generalized exponential distribution was suggested by Hossain and Ahsanullah [5]. Some important aspects of this distribution in the area of estimation remain unexplored in the earlier works. We discuss here the maximum likelihood (ML) method and the method of moments to estimate the parameters. The sufficient condition for the existence of a unique solution of the parameters obtained by the method of moments is derived. Finally, a popular real life numerical example is illustrated to investigate the application of both methods of estimation and the results obtained therein are compared with four similar well known three-parameter distributions.

Keywords

• Generalized exponential distribution
• Maximum Likelihood Estimation
• Method of Moments
• Moment generating function
• Sufficient condition