Neutrosophic ratio-type estimators for estimating the population mean

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 $${Z}_{N}={Z}_{L}+{Z}_{U}{I}_{N}\, {\rm where}\, {I}_{N}\in \left[{I}_{L}, {I}_{U}\right], {Z}_{N}\in [{Z}_{l}, {Z}_{u}]$$ Z N = Z L + Z U I N where I N ∈ I L , I U , Z N ∈ [ 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.

Ratio-Type Estimator for Estimating the Neutrosophic Population Mean in Simple Random Sampling under Intuitionistic Fuzzy Cost Function

“…. , 26) have higher efficiency than the existing exponential neutrosophic estimators ȳBTrRN and ȳRrN for all three simulated populations. Among ȳNETi (i = 1, 2, .…”

“…Ref. [26] proposed the neutrosophic ratio estimators for the estimation of the neutrosophic population mean given in ( 9), ( 11), (13), and (15) below.…”

“…3. The third neutrosophic data set, containing 3000 values, is generated from N N (µ N , Σ N ) with µ N = ( [11,26], [13,28]) and…”

“…Ref. [26] proposed neutrosophic ratio and exponential ratio estimators for the estimation of the neutrosophic population mean in simple random sampling under the given sample size. Ref.…”

On Efficient Estimation of the Population Mean under Stratified Ranked Set Sampling

“…Aslam [27] suggested the neutrosophic statistical test for counts in climatology. Tahir et al [28] investigated neutrosophic ratio-type estimators for estimating the population mean. Recently, Vishwakarma and Singh [29] introduced a generalized estimator for computation of the population mean under neutrosophic RSS with an application to solar energy data.…”