A Refined Population Mean Estimator Using Median and Skewness: Applications to Breast Cancer and Brain Tumor Data

N. Venkata  Lakshmi; Faizan  Danish; Mustafa Ibrahim  Ahmed Araibi; I.  Elbatal; Ehab M.  Almetwally; Ahmed M.  Gemeay; Sonali Kedar  Powar; Aafaq A.  Rather

doi:10.6000/1929-6029.2025.14.36

Authors

N. Venkata Lakshmi Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology-Andhra Pradesh (VIT- AP) University, Inavolu, Beside AP Secretariat, Amaravati AP-522237, India
Faizan Danish Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology-Andhra Pradesh (VIT- AP) University, Inavolu, Beside AP Secretariat, Amaravati AP-522237, India
Mustafa Ibrahim Ahmed Araibi Department of Business Admiration, College of Business, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia
I. Elbatal Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia
Ehab M. Almetwally Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia
Ahmed M. Gemeay Department of Mathematics, Faculty of Science, Tanta University, Tanta 31527, Egypt
Sonali Kedar Powar Department of Computer Science, Faculty of Science and Technology, Vishwakarma University, Pune, India
Aafaq A. Rather Symbiosis Statistical Institute, Symbiosis International (Deemed University), Pune-411004, India https://orcid.org/0000-0001-8962-1660

DOI:

https://doi.org/10.6000/1929-6029.2025.14.36

Keywords:

Ratio-estimator, Simple Random Sampling, Mean Square Error

Abstract

Estimators are essential to sampling theory because they allow researchers and statisticians to calculate estimates of population parameters from observed data. In every survey activity, the experimenter aims to use methods that will improve the precision of population parameter estimations throughout both the design and estimation phases. When auxiliary data is used in the estimating, design, or both processes, these estimated precisions can be attained. By linearly merging the central value of the data under consideration with the skewness coefficient provided by Karl Pearson, this study created a new, improved predictor for calculating the average of a population. Estimators are crucial to sampling theory because of their capacity to produce estimates of population parameters from observed data.

In this work, a novel modified ratio-type estimator was constructed by linearly merging Karl-Pearson's coefficient of skewness with the median value. Simple random sampling (SRS) was the technique employed in this present study. We conduct a numerical analysis from the standpoint of real estate. Additionally, we do some real data analysis on two distinct cancers: the brain tumor dataset and the breast cancer dataset. The results of the simulation study, real data application in the medical field, and numerical investigation show that the suggested estimator achieves lower error when the median value and Karl Pearson's coefficient of skewness are combined. Furthermore, compared to the other estimators under consideration, the one proposed in this study achieves better precision.

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