The exp-$G$ family of probability distributions

Details The exp-$G$ family of probability distributions The exp-$G$ family of probability distributions

2010-03-08

arxiv.org/abs/1003.1727v1

Statistics

Methodology

A much improved version of the pioneering manuscript "A new family of distributions based on the trucanted exponential distrib

Scientific paper

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 showed that the new distribution have the reference distribution as special case, and that the usual inference procedures also hold in this case. Furthermore, we applied our method to yield three-parameter extensions of the Weibull and beta distributions. To motivate the use of our class of distributions, we present a successful application to fatigue life data.

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