The study focuses on the development of a new probability distribution with applications to extreme values. The distribution is proposed by incorporating an additional parameter into the inverse Pareto distribution using the α-Power Transformation. Various properties of the new distribution are derived. The paper also explores the estimation of the parameters by the Maximum Likelihood Estimation (MLE) technique. Simulations are performed to evaluate the performance of the MLEs. In addition, two real data sets with extreme values are used to evaluate the efficacy of the proposed model. It is concluded that the proposed model performs well in the case of extreme values compared to the existing distributions.

中文翻译：

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使用 Alpha 幂逆帕累托分布对极值建模

该研究的重点是开发一种新的概率分布，并将其应用于极值。该分布是通过使用 α 幂变换将附加参数合并到逆帕累托分布中提出的。导出了新分布的各种属性。本文还探讨了最大似然估计 (MLE) 技术对参数的估计。执行模拟以评估 MLE 的性能。此外，使用两个具有极值的真实数据集来评估所提出模型的功效。得出的结论是，与现有分布相比，所提出的模型在极值情况下表现良好。