Aljohani Hassan M
Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia.
Heliyon. 2024 Feb 27;10(5):e26893. doi: 10.1016/j.heliyon.2024.e26893. eCollection 2024 Mar 15.
Working on symmetrical or asymmetrical data is complicated since each requires a different probability density function. Many statistical distributions can be used for these data types, where choosing one should be satisfied with the correct data type. So, we apply the ranked set sampling technique, which is essential in gaining data when dealing with units in a population is expensive. However, their classification is simple according to the variable of interest. The Unit Generalized Rayleigh distribution has recently played a crucial role in analyzing symmetrical or asymmetrical complex data sets specifically in modeling claim and risk data used in actuarial and financial studies, and its density can take different symmetric and asymmetric possible shapes. It is proposed in various areas, such as reliability, survival, economics, actuarial science, and insurance. We applied the ranked set sampling design in this article for gaining the model parameter estimations of the unit generalized Rayleigh model. Different estimation procedures and risk measures are computed. Moreover, the performance of these measures is illustrated via numerical simulation experiments. Under different proposed estimators, we conduct the validation of the suggested ranked set sampling design via numerous Monte Carlo simulation experiments by computing average bias and mean squared errors. At the end, we illustrated two real applications of the financial area for demonstrating the potential and the supremacy of the proposed ranked set sampling estimators.
处理对称或非对称数据很复杂，因为每种数据都需要不同的概率密度函数。许多统计分布可用于这些数据类型，选择时应与正确的数据类型相匹配。因此，我们应用排序集抽样技术，当处理总体中的单位成本很高时，该技术对于获取数据至关重要。然而，根据感兴趣的变量，它们的分类很简单。单位广义瑞利分布最近在分析对称或非对称复杂数据集方面发挥了关键作用，特别是在精算和金融研究中对索赔和风险数据进行建模时，其密度可以呈现不同的对称和非对称可能形状。它在可靠性、生存、经济、精算科学和保险等各个领域都有应用。在本文中，我们应用排序集抽样设计来获取单位广义瑞利模型的模型参数估计值。计算了不同的估计程序和风险度量。此外，通过数值模拟实验说明了这些度量的性能。在不同的提议估计量下，我们通过计算平均偏差和均方误差，通过大量蒙特卡罗模拟实验对建议的排序集抽样设计进行验证。最后，我们展示了金融领域的两个实际应用，以证明所提议的排序集抽样估计量的潜力和优越性。
