Research Article On Extended Neoteric Ranked Set Sampling Plan: Likelihood Function Derivation and Parameter Estimation Fathy H. Riad, 1,2 Mohamed A. Sabry , 2 Ehab M. Almetwally , 3,4 Ramy Aldallal , 5 Randa Alharbi , 6 and Md. Moyazzem Hossain 7 1 Mathematics Department, College of Science, Jouf University, P. O.Box 2014, Sakaka, Saudi Arabia 2 Department of Mathematics, Faculty of Science, Minia University, Minia 61519, Egypt 3 Department of Mathematical Statistics, Faculty of Graduate Studies for Statistical Research, Cairo University, Cairo, Egypt 4 Faculty of Business Administration, Delta University of Science and Technology, Gamasa, Egypt 5 College of Business Administration in Hotat Bani Tamim, Prince Sattam Bin Abdulaziz University, Al-Kharj, Saudi Arabia 6 Department of Statistics, Faculty of Science, University of Tabuk, Tabuk, Saudi Arabia 7 Department of Statistics, Jahangirnagar University, Savar, Dhaka 1342, Bangladesh Correspondence should be addressed to Mohamed A. Sabry; mohusss@cu.edu.eg and Md. Moyazzem Hossain; hossainmm@juniv.edu Received 16 November 2021; Revised 13 April 2022; Accepted 21 April 2022; Published 2 June 2022 Academic Editor: M. M. El-Dessoky Copyright © 2022 Fathy H. Riad et al. is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. e extended neoteric ranked set sampling (ENRSS) plan proposed by Taconeli and Cabral has proven to outperform many one stages and two stages ranked set sampling plans when estimating the mean and the variance for different populations. erefore, in this paper, the likelihood function based on ENRSS is proposed and used for estimation of the parameters of the inverted Nadarajah–Haghighi distribution. An extensive Monte Carlo simulation study is conducted to assess the performance of the proposed likelihood function, and the efficiency of the estimated parameters based on ENRSS is compared with the well-known ranked set sampling (RSS) plan and some of its modifications. ese modifications include the extended ranked set sampling (ERSS) plan and the neoteric ranked set sampling (NRSS) plan. e results as foreseeable were very satisfactory and gave similar results to Taconeli and Cabral’s 2019 results. 1. Introduction Ranked set sampling (RSS) plans were proposed to provide estimators that are more efficient than those derived under simple random sampling (SRS) plans. RSS plans were first proposed by McIntyre in 1952, to find efficient estimates of the mean pasture yields. ese plans assume that there are no errors in ranking the units concerning the variable of interest. In most practical applications, imperfect ranking exists and there will be an efficiency loss in the estimators [1]. To reduce such losses, several modifications to the RSS procedure were proposed. e main purpose was to allow for the achievement of higher statistical efficiency and probably a lower operating effort. e first modification of RSS was the extreme ranked set sampling (ERSS) plan introduced by Samwai et al. [2]. Muttlak [3] proposed the median ranked set sampling (MRSS) plan, Al-Odat and Al-Saleh [4] pro- posed the moving extreme ranked set sampling (MERSS) plan, Al-Saleh and Al-Omari [5] proposed the multistage ranked set sampling (MSRSS), and others proposed the multistage ranked set sampling (MSRSS). Recently, Zamanzade E, Al-Omari [1] proposed a new ranked set sampling plan based on a dependent scheme, namely, the neoteric ranked set sampling (NRSS) plan which showed relative improvement in the efficiency of the population mean and variance estimates. Moreover, Taconeli and Cabral [6] proposed several modifications to the NRSS plan. One of these plans is the extended neoteric ranked set sampling (ENRSS) plan. ey showed that the ENRSS plan is superior to NRSS and other plans. Unlike RSS and ERSS plans, NRSS and ENRSS are classified as dependent RSS plans as the resulting samples have a dependence structure. Hindawi Complexity Volume 2022, Article ID 1697481, 13 pages https://doi.org/10.1155/2022/1697481