Transformed Naive Ratio and Product Based Estimators for Estimating Population Mode in Simple Random Sampling

TL;DR

This paper introduces transformed naive ratio and product estimators for estimating the population mode in simple random sampling, demonstrating improved efficiency over traditional estimators through theoretical and simulation analysis.

Contribution

It proposes novel transformed estimators for population mode estimation using auxiliary information, enhancing efficiency over existing naive methods.

Findings

Proposed estimators show lower bias and mean square error.

Transformations improve estimator efficiency in both real and artificial data.

Confidence intervals indicate better coverage with the new estimators.

Abstract

In this paper, we propose a transformed na\"ive ratio and product based estimators using the characterizing scalar in presence of auxiliary information of the study variable for estimating the population mode following simple random sampling without replacement. The bias, mean square errors, relative efficiency, ratios of the exact values of mean square errors to the simulated mean square errors and confidence interval are studied for the performance of the proposed transformed na\"ive ratio type estimator with the certain natural population as well as artificially generated data sets. We have shown that proposed transformed na\"ive ratio based estimator is more efficient than the na\"ive estimator and na\"ive ratio estimator of the population mode.