Neutrosophic ratio-type estimators for estimating the population mean

Zaigham Tahir,Javid Shabbir,Hina Khan,Florentin Smarandache,Muhammad Aslam,Yasar Mahmood

doi:10.1007/s40747-021-00439-1

Abstract

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.

Highlights

Data in classical statistics are known and formed by crisp numbers
The analysis by simulated neutrosophic data verifies that the estimator yKNN is most efficient, while the estimators yBT r N and yRrn(a 1, b 1) are precisely efficient. yRr N (a 0, b 0) becomes a simple ratio estimator of mean, so it is better than others after yKNN
The present study aims to use the ratio estimation method under neutrosophic data derived from simple random sampling

Summary

Introduction

Data in classical statistics are known and formed by crisp numbers. Many authors worked on several estimators for estimating the mean of the finite population in the existence of auxiliary information under classical statistics. “The study suggested that in the presence of high correlation between the study variable and auxiliary variable, we get significantly low sampling error for ratio, instead of taking the study variable only and we may need less sampling for ratio estimation method or the ratio estimation method reduces the sample size providing equal precision [13]”. A detailed discussion on ratio estimation and its properties and examples were present in one study One study discussed the applications of a ratio-type estimator for multivariate k-statistics [23]. More studies and various uses and types of ratio-type estimation techniques devel-

Methods

Discussion

Conclusion