The exp-$G$ family of probability distributions

Abstract

In this paper we introduce a new method to add a parameter to a family of distributions. The additional parameter is completely studied and a full description of its behaviour in the distribution is given. We obtain several mathematical properties of the new class of distributions such as Kullback–Leibler divergence, Shannon entropy, moments, order statistics, estimation of the parameters and inference for large sample. Further, we show that the new distribution has the reference distribution as special case, and that the usual inference procedures also hold in this case. We present a comprehensive study of two special cases of the exp-$G$ class: exp-Weibull and exp-beta distributions. Further, an application to the real data set is presented. This family also opens a wide variety of research, as the authors may develop its special cases in full detail.