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.
Highlights
One of the most popularly used sampling methods is Ranked Set Sampling (RSS)
It is theoretically shown that these estimators are consistent to the population cumulative distribution function (CDF) F(t)
By incorporating the information generated from the unmeasured sampling items, a general class of CDF estimators is constructed which enables us to develop our proposed estimators
Summary
One of the most popularly used sampling methods is Ranked Set Sampling (RSS). As, it is very helpful in the situations where ranking can be done at a cost that is not problematic relative to the cost of making accurate quantification on the interested variable. The rounded parentheses of Yi(i:m)j implies that the perfect ranking situation is assumed In such cases, for a fixed j, Yi(i:m)j follows the distribution of the ith order statistic from a sample of size m. Step 5: Select this time the (m1 − v + 1)th smallest ranked unit from each of the k sets obtained by Step 4. Step 7: Select the ith smallest ranked unit from each (m − 2k) sets obtained by Step 6, where i = k + 1, ... Al-Omari (2021) studied maximum likelihood estimators of location-scale families under VLRSS and concluded that the VLRSS-based estimators tend to outperform their RSS analogues Motivated by these findings, we try to develop the envisaged CDF estimator under VLRSS.
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