A Generalization of the Exponential-Logarithmic Distribution

Abstract

A three-parameter lifetime distribution with increasing, decreasing, and unimodal failure rates is presented as a generalization of the exponential-logarithmic distribution introduced by Tahmasbi and Rezaei (2008). Various statistical properties and reliability aspects are explored and the estimation of parameters is studied, using the standard maximum likelihood procedures with complete data; the estimation is discussed briefly when some observations are randomly right-censored. Simulation results and applications of the model to real data are included.

AMS Subject Classification:

• 60E99
• 62N05

Keywords:

• Decreasing failure rate
• Entropy
• Exponential-logarithmic distribution
• Increasing failure rate
• Maximum likelihood estimation
• Mean residual lifetime
• Random censoring
• Unimodal failure rate

Acknowledgments

We thank an associate editor and two referees for their useful comments and suggestions.