A class of ratio-cum-product estimators of population mean under extreme ranked set sampling (ERSS) and simple random sampling (SRS)

Abstract

Extreme Ranked Set Sampling (ERSS) is a survey technique which seeks to improve the likelihood that collected sample data provides a good representation of the population and minimizes costs associated with obtaining them. The main goal of a statistical survey is to reduce sampling errors either by devising suitable sampling scheme or by formulating efficient estimator of the population parameters. In an attempt to address the problem of weak or loss of efficiency usually suffered in estimation of population mean under Simple Random Sampling (SRS), a class of ratio-cum-product estimators for population mean of the study variable Y is proposed based on ERSS using information on a single accompanying variable. Members of the proposed class of estimators were obtained by assigning various values to the scalars that helps in designing the estimators. These members were then transformed to a form that can be easily expanded using Taylor’s series approximation, from where various properties such as biases, relative biases, Mean Square Errors (MSEs), and Optimal Mean Square Errors (OMSEs) were derived under large sample approximation. Empirical study was conducted using three natural population data sets in order to investigate the performances and efficiency of the proposed classes of estimators under ERSS over its corresponding counterpart’s estimator based on SRS and some existing ratio and product estimators. This empirical study was followed up with a computer simulation study using R-software. The results revealed that the advocated class of estimators in ERSS produced smaller biases and MSEs which is an indicator of appreciable gain in efficiency and superiority over its corresponding counterpart estimator and some existing ratio type estimators in sample survey for all cases considered in this work and are therefore adjudged to provide a better alternative whenever efficiency is required.