标题： 概率分布的 exp-$G$族 显示英文标题

标题： The exp-$G$ family of probability distributions

摘要： 在本文中，我们引入了一种向分布族添加参数的新方法。 额外的参数得到了全面研究，并给出了其在分布中的行为的完整描述。 我们获得了新分布类的几个数学性质，如 Kullback-Leibler散度、Shannon熵、矩、顺序统计量、参数估计和大样本推断。 此外，我们证明了新分布具有参考分布作为特例，并且在这种情况下，常规的推断过程仍然适用。 此外，我们将我们的方法应用于获得Weibull和beta分布的三参数扩展。 为了说明我们分布类的使用，我们展示了一个成功应用于疲劳寿命数据的应用。 显示英文摘要

摘要： 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.