A New Compound Gamma and Lindley Distribution with Application to Failure Data

  • Mousa Abdi Department of Mathematics and computing, Higher Education Complex of Bam, Bam, Iran
  • Akbar Asgharzadeh
  • Hassan S. Bakouch
  • Zahra Alipour

Abstract

 In this paper, we propose a new lifetime distribution by compounding the gamma and Lindley distributions. Construction of it can be interpreted in the viewpoint of the reliability analysis and Bayesian inference. Moreover, the distribution has decreasing and unimodal hazard rate shapes. Several properties of the distribution are obtained, involving characteristics of the (reverse) hazard rate function, quantiles, moments, extreme order statistics and some stochastic order relations. Estimating the distribution parameters is discussed by some estimation methods and their performance is evaluated by a simulation study. Also, estimation of the stress-strength parameter is investigated. Usefulness of the distribution among other models is illustrated by fitting two failure data sets and using some goodness-of-fit measures.

Published
2019-01-26
How to Cite
Abdi, M., Asgharzadeh, A., Bakouch, H., & Alipour, Z. (2019). A New Compound Gamma and Lindley Distribution with Application to Failure Data. Austrian Journal of Statistics, 48(3), 54-75. https://doi.org/https://doi.org/10.17713/ajs.v48i3.843