Characteristics of the GLLE Family of Lifetime Distributions, and Applications

ABSTRACT. A Generalized Log-Logistic (GLL) family of lifetime distributions is one in which any pair of distributions are related through a GLL transformation, for some (non-negative) value of the transformation parameter (the odds function of the second distribution is the power of the odds function of the first distribution). We consider GLL families generated from an exponential distribution. We derive some useful characteristics of these distributions; moreover, we discuss the hazard rates and Kullback-Leibler divergence, then illustrate the usefulness of this distribution family by fitting real data sets.