On some life distributions with flexible failure rate

Abstract

A new three-parameter distribution family with a flexible failure rate function arising by mixing the Weibull distribution and power-series distribution is introduced. This distribution family includes special cases of some well-used mixing distributions and generalizes the exponential power-series distribution. Various properties of the new distribution family are discussed. The maximum likelihood estimation and an EM algorithm are presented for finding the estimates of the distribution family parameters, and expressions for their asymptotic variance and covariance are derived. Intensive simulation studies are implemented and experimental results are illustrated with real data-sets.

Keywords:

• EM algorithm
• failure rate function
• information matrix
• maximum likelihood estimation
• Power-series distribution

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Science Foundation of China [grant number 71101118], the Program for New Century Excellent Talents in University in China [grant number NCET-13-0961] and the Fundamental Research Funds for the Central Universities [grant number JBK150501].