Generalized Modified Ratio Estimators Using Kurtosis and Skewness under Simple Random Sampling with Replacement

Author(s)	Dr. VETRI SELVI P
Country	India
Abstract	This research proposes an advanced generalized class of modified ratio estimators for the estimation of finite population means, leveraging known auxiliary information such as Skewness (β1) and Kurtosis (β2). While traditional ratio estimators rely heavily on the linear relationship between variables, the proposed class incorporates higher-order moments to better capture the distributional characteristics of the auxiliary variable. Using the first-order Taylor series approximation, we derive explicit expressions for the Bias and Mean Squared Error (MSE) under Simple Random Sampling with Replacement (SRSWR). Furthermore, the study identifies the optimal conditions under which these estimators outperform the classical ratio and product estimators. To validate the theoretical framework, a comprehensive Monte Carlo simulation study was conducted, demonstrating that the proposed estimators provide significantly higher Percent Relative Efficiency (PRE), especially in the presence of non-normal auxiliary distributions.
Keywords	Auxiliary variable, Mean Squared Error (MSE), Skewness (β1) and Kurtosis (β2), Percent Relative Efficiency (PRE) and Simple Random Sampling with Replacement (SRSWR)
Field	Mathematics > Statistics
Published In	Volume 8, Issue 3, May-June 2026
Published On	2026-05-23
DOI	https://doi.org/10.36948/ijfmr.2026.v08i03.79326

About IJFMR Fees & Payment Current Issue Publication Archive	Submit Research Paper Track Submission Status Publication Guidelines Publication Ethics Peer Review & Plagiarism	Join as a Reviewer Editors & Reviewers Reviewer Referral Program Get Reviewer Membership Certi.	Website/Journal Policies Usage Policy Content Policies Privacy Policy

Contact Us		+91-9687-828-838	editor@ijfmr.com

International Journal For Multidisciplinary Research