A new lifetime model with different types of failure rate

A new class of lifetime distributions, which can exhibit with upside-down bathtub-shaped, bathtub-shaped, decreasing, and increasing failure rates, is introduced. The new distribution is constructed by compounding generalized Weibull and logarithmic distributions, leading to improvement on the lifetime distribution considered in Dimitrakopoulou et al. (2007 Dimitrakopoulou, T., K. Adamidis, and S. Loukas. 2007. A lifetime distribution with an upside-down bathtub-shaped hazard function. IEEE Transactions on Reliability 56:308–11.Crossref], Web of Science ®] , Google Scholar]) by having no restriction on the shape parameter and extending the result studied by Tahmasbi and Rezaei (2008 Tahmasbi, R., and S. Rezaei. 2008. A two-parameter lifetime distribution with decreasing failure rate. Computational Statistics and Data Analysis 52:3889–901.Crossref], Web of Science ®] , Google Scholar]) in the general form. The proposed model includes the exponential–logarithmic and Weibull–logarithmic distributions as special cases. Various statistical properties of the proposed class are discussed. Furthermore, estimation via the maximum likelihood method and the Fisher information matrix are discussed. Applications to real data demonstrate that the new class of distributions is more flexible than other recently proposed classes.