Estimation of the population distribution function using varied L ranked set sampling

Department of Quantitative Techniques, Faculty of Commerce, Aswan University, Aswan, Egypt

^* Corresponding author: mohamed_abdallah@com.aswu.edu.eg; statisticsms.2010@gmail.com

Received: 22 June 2021
Accepted: 4 February 2022

Abstract

A generalized ranked set sampling (RSS) plan has recently been provided in the literature called varied L RSS (VLRSS). It is shown that VLRSS encompasses several existing RSS variations and also it efficiently estimates the population mean. In this article, we extend the work and consider estimating the cumulative distribution function (CDF) using VLRSS. Three new CDF estimators are proposed and their asymptotic properties are also theoretically investigated. Taking into account the information supported by the unmeasured sampling units, we also propose a general class of CDF estimators. Using small Monte Carlo experiments, we study the behavior of the proposed CDF estimators with respect to the conventional CDF estimator under RSS. It is found that the conventional RSS-based CDF is outperformed by at least one of VLRSS-based CDF estimators in most of the considered cases. Finally, an empirical example is utilized to illustrate the potential application of the proposed estimators.