Department of Mathematics & Statistics, College of Science, Taif University, Taif, Saudi Arabia.
Department of Mathematics, College of Education, Misan University, Amarah, Iraq.
PLoS One. 2022 Oct 6;17(10):e0275001. doi: 10.1371/journal.pone.0275001. eCollection 2022.
In the present work, a class of distributions, called new extended family of heavy-tailed distributions is introduced. The special sub-models of the introduced family provide unimodal, bimodal, symmetric, and asymmetric density shapes. A special sub-model of the new family, called the new extended heavy-tailed Weibull (NEHTW) distribution, is studied in more detail. The NEHTW parameters have been estimated via eight classical estimation procedures. The performance of these methods have been explored using detailed simulation results which have been ordered, using partial and overall ranks, to determine the best estimation method. Two important risk measures are derived for the NEHTW distribution. To prove the usefulness of the two actuarial measures in financial sciences, a simulation study is conducted. Finally, the flexibility and importance of the NEHTW model are illustrated empirically using two real-life insurance data sets. Based on our study, we observe that the NEHTW distribution may be a good candidate for modeling financial and actuarial sciences data.
在本工作中，引入了一类分布，称为新的广义长尾分布族。所引入族的特殊子模型提供了单峰、双峰、对称和不对称的密度形状。新家族的一个特殊子模型，称为新广义重尾 Weibull（NEHTW）分布，进行了更详细的研究。通过八种经典估计程序对 NEHTW 参数进行了估计。使用详细的模拟结果来探索这些方法的性能，这些结果按偏序和总序进行了排序，以确定最佳估计方法。为 NEHTW 分布导出了两个重要的风险度量。为了证明这两个精算度量在金融科学中的有用性，进行了模拟研究。最后，使用两个实际的保险数据集进行实证说明 NEHTW 模型的灵活性和重要性。根据我们的研究，我们观察到 NEHTW 分布可能是金融和精算科学数据建模的一个很好的候选。
