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.
翻译：我们通过应用 alpha 功率转换,对 Pseudo- Lindley 分布进行新的概括化。 获取的分布被称作 Pseudo- Lindley 功率转换分布(\ textit{ PL- APT} ) 。 提供\ textit{ PL- APT} 分布的一些可移动数学属性, 包括可靠性、 危险率、 订单统计和寄生虫。 使用最大可能性方法来获取参数对\ textit{ PL- APT} 分布的估计。 正在讨论拟议分布的无症状特性。 此外, 还将进行模拟研究, 比较\ textit{ PL- APT} 与 Lindley 和 Pseuddo- Lindley 分布的建模能力和灵活性。 提供与 Lindley 和 Psedodododo- Lindley 分布相匹配的 。 最大可能性方法用于获取参数估计 。 发现\ textitit{ PLPL- APT} 的吸引力的极端区域,, 以及其孔状和 盘和 孔状的四角 函数功能。 最后, 以 统计图示 和图示 和图示的Lodal- 和图示的图示的图示 和图解的图解的Loslem 和图示的图示 和图示的Lodal- sl- sl 和图示的索引 。
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