A two parameter ratio-product-ratio estimator using auxiliary information

TL;DR

This paper introduces a new two-parameter estimator for population mean that combines ratio and product methods, demonstrating improved accuracy over traditional estimators through theoretical analysis and real data application.

Contribution

It develops a novel two-parameter ratio-product-ratio estimator and derives its bias and mean square error, showing conditions for its superiority over existing estimators.

Findings

Proposed estimator has lower mean square error under certain conditions.

The estimator outperforms traditional methods in groundwater data application.

Theoretical derivations support its efficiency improvements.

Abstract

We propose a two parameter ratio-product-ratio estimator for a finite population mean in a simple random sample without replacement following the methodology in Ray and Sahai (1980), Sahai and Ray (1980), Sahai and Sahai (1985) and Singh and Ruiz Espejo (2003). The bias and mean square error of our proposed estimator are obtained to the first degree of approximation. We derive conditions for the parameters under which the proposed estimator has smaller mean square error than the sample mean, ratio and product estimators. We carry out an application showing that the proposed estimator outperforms the traditional estimators using groundwater data taken from a geological site in the state of Florida.