一类新的非对称分布族用于轻尾右偏数据建模
A New Family of Asymmetric Distributions for Modeling Light-Tailed and Right-Skewed Data
摘要：
对于某些具有非对称密度函数且两端呈指数衰减的$α\geq0$，在$(α,\infty)$上定义了一个新的三参数累积分布函数.新的分布是接近熟悉的分布，如伽马和对数正态分布，但这个新的一个显示自己的元素，因此没有推广这些分布。因此，新的分布构成了一个新的替代拟合值显示轻尾行为。此外，这种新的分布显示出极大的灵活性，可以通过调整一些参数来拟合大量数据。我们将这种新分布称为广义指数对数平方分布（GEL-S）。GEL-S分布的统计性质进行了讨论。最大似然法提出了估计模型参数，但由于在操作的参数的困难，在计算过程中纳入适应。新的分布的性能进行了研究，使用模拟。来自不同领域的实际数据集的应用程序。
英文摘要：
A new three-parameter cumulative distribution function defined on $(α,\infty)$, for some $α\geq0$, with asymmetric probability density function and showing exponential decays at its both tails, is introduced. The new distribution is near to familiar distributions like the gamma and log-normal distributions, but this new one shows own elements and thus does not generalize neither of these distributions. Hence, the new distribution constitutes a new alternative to fit values showing light-tailed behaviors. Further, this new distribution shows great flexibility to fit the bulk of data by tuning some parameters. We refer to this new distribution as the generalized exponential log-squared distribution (GEL-S). Statistical properties of the GEL-S distribution are discussed. The maximum likelihood method is proposed for estimating the model parameters, but incorporating adaptations in computational procedures due to difficulties in the manipulation of the parameters. The perfomance of the new distribution is studied using simulations. Applications to real data sets coming from different domains are showed.
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