Generalized Neutrosophic Sampling Strategy for Elevated estimation of Population Mean

Abstract

One of the disadvantages of the point estimate in survey sampling is that it fluctuates from
sample to sample due to sampling error, as the estimator only provides a point value for the parameter
under discussion. The neutrosophic approach, pioneered by Florentin Smarandache, is an excellent tool
for estimating the parameters under consideration in sampling theory since it yields interval estimates in
which the parameter lies with a very high probability. As a result, the neutrosophic technique, which is a
generalization of classical approach, is used to deal with ambiguous, indeterminate, and uncertain data.
In this investigation, we suggest a new general family of ratio and exponential ratio type estimators for
the elevated estimation of neutrosophic population mean of the primary variable utilizing known
neutrosophic auxiliary parameters. For the first degree approximation, the bias and Mean Squared Error
(MSE) of the suggested estimators are computed. The neutrosophic optimum values of the characterizing
constants are determined, as well as the minimum value of the neutrosophic MSE of the suggested
estimator is obtained for these optimum values of the characterizing scalars. Because the minimum MSE
of the classical estimators of population mean lies inside the estimated interval of the neutrosophic
estimators, the neutrosophic estimators are better than the equivalent classical estimators. The empirical
investigation, which used both real and simulated data sets, backs up the theoretical findings. For
practical utility in various areas of applications, the estimator with the lowest MSE or highest Percentage
Relative Efficiency (PRE) is recommended.