伪Lindley α幂变换分布的数学刻画及渐近性质
The Pseudo-Lindley Alpha Power transformed distribution, mathematical characterizations and asymptotic properties
摘要：
我们引入了一个新的推广的伪林德利分布应用α幂变换。所获得的分布被称为伪林德利α幂变换分布（\textit{PL-APT}）。给出了\textit{PL-APT}分布的可靠度、危险率、顺序统计量和熵等数学性质。利用极大似然法得到了\textit{PL-APT}分布的参数估计。讨论了该分布的渐近性质。此外，模拟研究进行比较的建模能力和灵活性的\textit{PL-APT}与林德利和伪林德利分布。\textit{PL-APT}与Lindley分布和伪Lindley分布具有良好的拟合性。找到了\textit{PL-APT}的极值吸引区域，研究了它的分位数和极值分位数函数.最后，极值指数由双指标Hill估计器估计（Ngom和Lo，2016），并提供和表征了相关的渐近统计检验。
英文摘要：
We introduce a new generalization of the Pseudo-Lindley distribution by applying alpha power transformation. The obtained distribution is referred as the Pseudo-Lindley alpha power transformed distribution (\textit{PL-APT}). Some tractable mathematical properties of the \textit{PL-APT} distribution as reliability, hazard rate, order statistics and entropies are provided. The maximum likelihood method is used to obtain the parameters' estimation of the \textit{PL-APT} distribution. The asymptotic properties of the proposed distribution are discussed. Also, a simulation study is performed to compare the modeling capability and flexibility of \textit{PL-APT} with Lindley and Pseudo-Lindley distributions. The \textit{PL-APT} provides a good fit as the Lindley and the Pseudo-Lindley distribution. The extremal domain of attraction of \textit{PL-APT} is found and its quantile and extremal quantile functions studied. Finally, the extremal value index is estimated by the double-indexed Hill's estimator (Ngom and Lo, 2016) and related asymptotic statistical tests are provided and characterized.
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