A new family of compound exponentiated logarithmic distributions with applications to lifetime data

Abstract

Abstract The logarithmic distribution and a given lifetime distribution are compounded to construct a new family of lifetime distributions. The compounding is performed with respect to maxima. Expressions are derived for lifetime properties like moments and the behavior of extreme values. Estimation procedures for the method of maximum likelihood are also derived and their performance assessed by a simulation study. Three real data (including two lifetime data) applications are described that show superior performance (assessed with respect to Kolmogorov Smirnov statistics, likelihood values, AIC values, BIC values, probability-probability plots and density plots) versus at least five known lifetime models, with each model having the same number of parameters as the model it is compared to.