Enhanced Ratio-Type Population Variance Estimator Including Excess Kurtosis and Known Median of an Auxiliary Variable

Chandni Kumari
Abstract

We propose a ratio‑type estimator for population variance that leverages known auxiliary‑variable median ( 𝑀𝑥) and excess kurtosis ( 𝐾𝑥). Derivations of bias and Mean Squared Error (MSE) via first‑order Taylor series are presented. Analytical efficiency conditions show it outperforms traditional unbiased estimators and earlier ratio‑type methods. A numerical analysis indicates that the suggested estimator performs well in terms of a reduced mean squared error.

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