Inverse Weibull power series distributions: properties and applications

Abstract

Inverse Weibull (IW) distribution is one of the widely used probability distributions for nonnegative data modelling, specifically, for describing degradation phenomena of mechanical components. In this paper, by compounding IW and power series distributions we introduce a new lifetime distribution. The compounding procedure follows the same set-up carried out by Adamidis and Loukas [A lifetime distribution with decreasing failure rate. Stat Probab Lett. 1998;39:35–42]. We provide mathematical properties of this new distribution such as moments, estimation by maximum likelihood with censored data, inference for a large sample and the EM algorithm to determine the maximum likelihood estimates of the parameters. Furthermore, we characterize the proposed distributions using a simple relationship between two truncated moments and maximum entropy principle under suitable constraints. Finally, to show the flexibility of this type of distributions, we demonstrate applications of two real data sets.

Keywords:

• EM-algorithm
• Shannon entropy
• stochastic ordering

Mathematics Subject Classification:

• Primary: 62E15
• Secondary: 62F10

Acknowledgements

The authors are grateful to the editor and three anonymous referees for their many helpful comments and suggestions on an earlier version of this paper which led to this improved version.

Disclosure statement

No potential conflict of interest was reported by the authors.