A complementary generalized linear failure rate-geometric distribution

ABSTRACT

In this article, we shall attempt to introduce a new class of lifetime distributions, which enfolds several known distributions such as the generalized linear failure rate distribution and covers both positive as well as negative skewed data. This new four-parameter distribution allows for flexible hazard rate behavior. Indeed, the hazard rate function here can be increasing, decreasing, bathtub-shaped, or upside-down bathtub-shaped. We shall first study some basic distributional properties of the new model such as the cumulative distribution function, the density of the order statistics, their moments, and Rényi entropy. Estimation of the stress-strength parameter as an important reliability property is also studied. The maximum likelihood estimation procedure for complete and censored data and Bayesian method are used for estimating the parameters involved. Finally, application of the new model to three real datasets is illustrated to show the flexibility and potential of the new model compared to rival models.

Keywords:

• Censoring
• Exponential distribution
• Geometric distribution
• Hazard rate function
• Maximum likelihood estimation
• Mixing
• Stress-strength parameter

Mathematics Subject Classification:

• Primary 60E05; Secondary 62E15