Usman Mahamood, Singh Garib Nath, Kumar M S Jagadeesh, Basha S M Afsar
Department of Mathematics, (School of Advanced Sciences), Vellore Institute of Technology, Vellore 632014, India.
Department of Mathematics & Computing Indian Institute of Technology, (Indian School of Mines), Dhanbad 826007, India.
Heliyon. 2024 Sep 3;10(18):e37232. doi: 10.1016/j.heliyon.2024.e37232. eCollection 2024 Sep 30.
In the present work, we have proposed a novel general class of estimators for the estimation of population distribution function in two distinct situations of non-response. The estimation of distribution function (DF) may play an important role in environmental sciences such as in modelling the annual data of atmospheric NOx temporal concentration, drug removal rates from the body, to present the distribution of gene expression levels across cells etc. Similarly, it may also be useful in other environmental data like groundwater quality, rainfall, wind speed, river discharges, etc. for effective analysis leading to predictive modelling. In this study, it is shown that the suggested estimators of DF are among the best of all other considered estimators. Some estimators are also derived from the proposed family by choosing the suitable values of constants used. Theoretical comparisons of the proposed family of estimators with other family of estimators have been discussed. An empirical study based on two real data sets from literature has been conducted where it has been found that the performance of the proposed family of estimators is superior in terms of enhanced percentage relative efficiencies (PREs) than other family of estimators considered in this study. Further, a simulation study is also carried out which validates the competency behaviour of suggested estimators.
在本研究中，我们针对两种不同的无应答情况，提出了一类新颖的用于估计总体分布函数的通用估计量。分布函数（DF）的估计在环境科学中可能发挥重要作用，例如在模拟大气中氮氧化物时间浓度的年度数据、药物从体内的清除率、呈现基因表达水平在细胞间的分布等方面。同样，它在其他环境数据如地下水质量、降雨量、风速、河流流量等方面，对于进行有效分析以实现预测建模也可能是有用的。在本研究中，结果表明所建议的DF估计量在所有其他考虑的估计量中是最优的。通过选择所使用常数的合适值，还从所提出的族中导出了一些估计量。讨论了所提出的估计量族与其他估计量族的理论比较。基于文献中的两个真实数据集进行了实证研究，结果发现，在所考虑的增强相对效率百分比（PREs）方面，所提出估计量族的性能优于本研究中的其他估计量族。此外，还进行了一项模拟研究，验证了所建议估计量的性能表现。
