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Neutrosophic ratio-type estimators for estimating the population mean
Complex & Intelligent Systems ( IF 5.8 ) Pub Date : 2021-08-09 , DOI: 10.1007/s40747-021-00439-1
Zaigham Tahir 1 , Hina Khan 1 , Yasar Mahmood 1 , Muhammad Aslam 2 , Javid Shabbir 3 , Florentin Smarandache 4
Affiliation  

All researches, under classical statistics, are based on determinate, crisp data to estimate the mean of the population when auxiliary information is available. Such estimates often are biased. The goal is to find the best estimates for the unknown value of the population mean with minimum mean square error (MSE). The neutrosophic statistics, generalization of classical statistics tackles vague, indeterminate, uncertain information. Thus, for the first time under neutrosophic statistics, to overcome the issues of estimation of the population mean of neutrosophic data, we have developed the neutrosophic ratio-type estimators for estimating the mean of the finite population utilizing auxiliary information. The neutrosophic observation is of the form \({Z}_{N}={Z}_{L}+{Z}_{U}{I}_{N}\, {\rm where}\, {I}_{N}\in \left[{I}_{L}, {I}_{U}\right], {Z}_{N}\in [{Z}_{l}, {Z}_{u}]\). The proposed estimators are very helpful to compute results when dealing with ambiguous, vague, and neutrosophic-type data. The results of these estimators are not single-valued but provide an interval form in which our population parameter may have more chance to lie. It increases the efficiency of the estimators, since we have an estimated interval that contains the unknown value of the population mean provided a minimum MSE. The efficiency of the proposed neutrosophic ratio-type estimators is also discussed using neutrosophic data of temperature and also by using simulation. A comparison is also conducted to illustrate the usefulness of Neutrosophic Ratio-type estimators over the classical estimators.



中文翻译:

用于估计总体均值的中智比率型估计量

在经典统计下,所有研究都基于确定的、清晰的数据,以在有辅助信息时估计总体的均值。这种估计通常是有偏差的。目标是找到具有最小均方误差 (MSE) 的总体均值未知值的最佳估计值。中智统计学,经典统计学的概括处理模糊的、不确定的、不确定的信息。因此,第一次在中智统计下,为了克服中智数据总体均值估计的问题,我们开发了中智比率型估计器,用于利用辅助信息估计有限总体均值。中智观察的形式是\({Z}_{N}={Z}_{L}+{Z}_{U}{I}_{N}\, {\rm where}\, {I}_{N}\in \left[{I}_{L}, {I}_{U}\right], {Z}_{N}\in [{Z}_{l}, {Z}_{u}]\). 在处理模棱两可的、模糊的和中智类型的数据时,所提出的估计器对计算结果非常有帮助。这些估计量的结果不是单值的,而是提供了一种区间形式,其中我们的总体参数可能有更多的机会撒谎。它提高了估计器的效率,因为我们有一个估计区间,其中包含提供最小 MSE 的总体均值的未知值。还使用温度的中智学数据和模拟讨论了所提出的中智学比率型估计器的效率。还进行了比较以说明 Neutrosophic Ratio 型估计量相对于经典估计量的有用性。

更新日期:2021-08-09
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