Generalized Linear Failure Rate Distribution

Abstract

The exponential and Rayleigh are the two most commonly used distributions for analyzing lifetime data. These distributions have several desirable properties and nice physical interpretations. Unfortunately, the exponential distribution only has constant failure rate and the Rayleigh distribution has increasing failure rate. The linear failure rate distribution generalizes both these distributions which may have non increasing hazard function also. This article introduces a new distribution, which generalizes linear failure rate distribution. This distribution generalizes the well-known (1) exponential distribution, (2) linear failure rate distribution, (3) generalized exponential distribution, and (4) generalized Rayleigh distribution. The properties of this distribution are discussed in this article. The maximum likelihood estimates of the unknown parameters are obtained. A real data set is analyzed and it is observed that the present distribution can provide a better fit than some other very well-known distributions.

Keywords:

• Generalized exponential distribution
• Generalized Rayleigh distri-bution
• Linear failure rate distribution
• Maximum likelihood method

Mathematics Subject Classification:

• 46N30
• 47N30
• 65C60

Acknowledgments

The authors would like to thank two referees and the Associate Editor for many constructive suggestions.