Authors

• Ali Akbar Jafari
• Eisa Mahmoudi

Department of Statistics, Yazd University, Yazd, Iran.

Abstract

We introduce in this paper a new four-parameter generalized version of the linear failure rate distribution which is called Beta-linear
failure rate distribution. The new distribution is quite flexible and can be used effectively in modeling survival data and reliability problems. It can have a constant, decreasing, increasing and bathtub-shaped failure rate function depending on its parameters. It includes some well-known lifetime distributions as special sub-models. We provide a comprehensive account of the mathematical properties of the new distribution. In particular, A closed form expressions for the probability density, cumulative distribution and hazard rate functions of this new distribution is given. Also, the rth order moment of this distribution is derived. We discuss the maximum likelihood estimation of the unknown parameters of the new model for complete data and obtain an expression for the Fisher information matrix. In the end, to show the flexibility of the new distribution and illustrative purposes, an application using a real data set is presented.

Keywords

• Beta distribution
• hazard function
• linear failure rate distribution
• Maximum likelihood estimation
• moments
• Simulation