Ranked Set Sampling Methods Research Articles

Efficiency study of a robust regression-type estimator for population mean under different ranked set sampling methods with outlier handling

Efficiency study of a robust regression-type estimator for population mean under different ranked set sampling methods with outlier handling

An Efficient Variant of Ranked Set Sampling, Probability Proportional to Size with Application to Economic Data

In this paper, we apply the Ranked Set Sampling (RSS) technique to economic data in the form of homescan market research data set for the meat food group. The RSS method is then extended to select sampling units based on the Probability-Proportional-to-Size (PPS) approach. The new proposed ranked set sampling, using the PPS-derived method, RPPS, is assessed via Monte Carlo investigations and an extensive homescan data set to evaluate its performances. The results are promising and in line with theoretical and simulation studies, showing that the RPPS technique is more reliable and has a smaller variance than the PPS route.

Data-Driven Dynamic Optimization for Real-Time Parking Reservation Considering Parking Unpunctuality

This paper examines a real-time parking reservation service that dynamically allocates a limited number of parking slots (which can be reused) to serve parking requests in a crowded area. The study takes into account two stochastic factors: (i) random arrivals of parking requests and (ii) driver parking unpunctuality, which are seldom simultaneously considered in the existing literature. This study formulates the dynamic parking resource allocation problem as a joint chance-constrained model to maximize the expected total revenue over a finite horizon. Due to the complex nature of the model considering the two stochastic factors, the study proposes a data-driven approach using joint chance constraint decomposition and sample average approximation to approximate the model to a deterministic mixed-integer programming model. Furthermore, a stratified ranked set sampling method is introduced to construct a high-quality sample set as the input to the deterministic model, and valid inequalities are designed to accelerate the solution process. Numerical experiments based on real-world data are conducted to validate the performance of the proposed approach under multiple parking scenarios and provide findings.

Two-stage approximation allocation approach for real-time parking reservations considering stochastic requests and reusable resources

The digital economy has greatly impacted the traditional parking industry. This study focuses on a real-time parking reservation system that allocates available parking slots (supplies) to serve the parking requests (demands) of drivers within a certain area. The challenge lies in dealing with the randomness of requests with varying parking durations and the reusability of parking resources, which have not been well researched. To address this problem, we propose a stochastic optimization model and a data-driven two-stage approximation approach. The first stage generates a pre-allocation scheme as a basis, while the second stage dynamically adjusts the scheme based on observed requests and available parking slots to improve the system’s performance throughout a finite operational horizon. The study has three main contributions. Firstly, this paper proposes a data-driven nonparametric approach based on sample average approximation (SAA) to solve the stochastic optimization model. Secondly, it develops a stratified ranked set sampling (SRSS) method to ensure the quality of the sample set and proves that the sample set sampled by the SRSS method is unbiased. Finally, an evaluation method is proposed to establish a confidence interval for the expected revenue obtained by the data-driven method. Experimental results based on real parking demand data show that our approach outperforms both a commonly used heuristic allocation policy in the parking industry and the standard SAA approach with two popular sampling methods and an evaluation method based on Student’s T-test in the literature.

Adaptive EWMA control chart for monitoring the coefficient of variation under ranked set sampling schemes

In this study, we introduce an Adaptive Exponentially Weighted Moving based Coefficient of Variation (AEWMCV) control chart, designed to address situations where the process mean fluctuates over time and the standard deviation of the process changes linearly with the process mean. To enhance the efficiency and effectiveness of the control chart, we integrate the ranked set sampling method and its modified schemes, such as Simple Random Sampling, Quartile RSS, Median RSS, and Extreme RSS. The performance of the proposed AEWMCV control chart and the studied CV control charts are evaluated using the Average Run Length and Standard Deviation of Run Length metrics. Our findings reveal that the proposed control chart outperforms the existing CV control charts, especially in detecting slight to moderate changes in the process CV. To illustrate the practical applicability of the suggested control chart, we present an example demonstrating its use on a real dataset. The results highlight the superior performance of the AEWMCV control chart in accurately detecting and responding to changes in the process CV. In conclusion, our study introduces an innovative AEWMCV control chart that combines ranked set sampling and its modified schemes to enhance performance in scenarios with fluctuating process means and changing standard deviations. The proposed control chart proves to be more effective in detecting subtle variations in the process CV compared to traditional CV control charts. This research provides a valuable contribution to the field of control chart methodology, especially when dealing with challenging or costly data collection scenarios.

Different estimation methods for the generalized unit half-logistic geometric distribution: Using ranked set sampling

The generalized unit half-logistic geometric distribution (GUHLGD) is a modern two-parameter unit distribution with attractive shape flexibility for the corresponding probability density and hazard rate functions. Due to its versatility, it may be used to model a variety of current bounded real-world datasets. On the other hand, an effective sampling strategy for both parametric and non-parametric inferences is the ranked set sampling (RSS) method. This article focuses on estimating the parameters of the GUHLGD based on the RSS method as well as the simple random sampling (SRS) method. Eleven traditional estimation methods are taken into consideration, including the percentile, Cramér–von Mises, maximum likelihood, Anderson–Darling, right-tailed Anderson–Darling, left-tailed Anderson–Darling, least squares, weighted least squares, minimum spacing absolute-log distance, maximum product of spacing, and minimum spacing absolute distance methods. A Monte Carlo simulation is employed to compare the performance of the resultant estimates based on some accuracy measures. We draw the conclusion that, for both sampling procedures, the maximum likelihood estimation methodology is the best option among the rest based on the partial and total ranking measures. The estimates based on the RSS method are more efficient than the others based on the SRS method. Results from actual data further support the advantage of the RSS design over the SRS design.

Reevaluating the performance of control charts based on ranked-set sampling

Nearly one hundred types of control charts have been proposed that incorporate ranked-set sampling (RSS) methods. The performance of these charts has been evaluated with comparisons to existing charts based on simple random sampling. The reduction of the standard error in estimating the parameter being monitored with RSS leads to uniformly better average run length performance. We show, however, that these performance comparisons can be very misleading once the sampling strategy over time is considered more carefully with the benefits of RSS being considerably overstated. We consider the most basic RSS method when monitoring the mean of the process, but the approach can be applied to evaluate other RSS monitoring methods.

Evaluation of Ranked Set Sampling Methods under Skewed and Unskewed Distributions

Evaluation of Ranked Set Sampling Methods under Skewed and Unskewed Distributions

Half Logistic Inverted Nadarajah–Haghighi Distribution under Ranked Set Sampling with Applications

In this paper, we present the half logistic inverted Nadarajah–Haghigh (HL-INH) distribution, a novel extension of the inverted Nadarajah–Haghigh (INH) distribution. The probability density function (PDF) for the HL-INH distribution might have a unimodal, right skewness, or heavy-tailed shape for numerous parameter values; however, the shape forms of the hazard rate function (HRF) for the HL-INH distribution may be decreasing. Four specific entropy measurements were investigated. Some useful expansions for the HL-INH distribution were investigated. Several statistical and computational features of the HL-INH distribution were calculated. Using simple (SRS) and ranked set sampling (RSS), the parameters for the HL-INH distribution were estimated using the maximum likelihood (ML) technique. A simulation analysis was executed in order to determine the model parameters of the HL-INH distribution using the SRS and RSS methods, and RSS was shown to be more efficient than SRS. We demonstrate that the HL-INH distribution is more adaptable than the INH distribution and other statistical distributions when utilizing three real-world datasets.

Estimation of population variance under ranked set sampling method by using the ratio of supplementary information with study variable.

In biological and medical research, the cost and collateral damage caused during the collection and measurement of a sample are the reasons behinda compromise on the inference with a fixed and accepted approximation error. The ranked set sampling (RSS) performs better in such scenarios, andthe use of auxiliary information even enhances the performance of the estimators. Inthis study, two generalized classes of estimatorsareproposedto estimate the population variance using RSS and information of auxiliary variable. The bias and mean square errors ofthe proposed classes of estimators are derived up to first order of approximation. Some special cases of one ofthe proposed class ofestimatorsare also considered in the presence of available population parameters. A simulation study was conductedto see the performance of the members of the proposed family by using various sample sizes. The real-life dataapplication is done to estimate the variance of gestational age of fetuses with supplementary information. The results showed that RSS design is a more accurate method than simple random sampling, to determine the population variance of hard-to-measure or destructive sampling units.

Modern Design and Analysis For Hit/Miss Probability of Detection Studies Using Profile Likelihood Ratio Confidence Intervals

To characterize the capability of an inspection system, indications from the system must be collected over a range of defect sizes. For flaw indications, insufficient sample size, overlap, or evenness between hit and miss indications may cause the probability of detection (POD) estimations to not exist or have high bias. Extensive simulations of representative Lognormal, Weibull, and Uniformly distributed data at varying levels of overlap, evenness, and sample size were fit using four modeling techniques: logistic regression, Firth’s Bias Adjusted Likelihood, the Lasso, and a ranked set sampling method from nonparametric statistics. Profile likelihood ratio confidence intervals were used instead of the standard Wald method to calculate a90/95. The probability of existence and the percent bias of the estimates provide recommendations for the ideal levels of overlap, evenness, modeling technique, and sample size requirements when designing a hit/miss POD study.

Bootstrap Approach for Testing More Than Two Population Means with Ranked Set Sampling

In this study, hypothesis test is investigated based on Bootstrap sample selection methods to compare more than two population means under Ranked Set Sampling. Bootstrap sample selection methods are obtained by adapting Hui’s sample selection methods for confidence interval. We also compare these adapted methods with bootstrap simple random sampling and bootstrap ranked set sampling methods using simulation study. Simulation study shows that adapted methods which proposed in this paper perform quite well.

Goodness-of-Fit Tests for Weighted Generalized Quasi-Lindley Distribution Using SRS and RSS with Applications to Real Data

This paper deals with the problem of goodness-of-fit tests (GFTs) for the weighted generalized quasi-Lindley distribution (WGQLD) using ranked set sampling (RSS) and simple random sampling (SRS) techniques. The tests are based on the empirical distribution function and sample entropy. These tests include the Kullback–Leibler, Kolomogorov–Smirnov, Anderson–Darling, Cramér–von Mises, Zhang, Liao, and Shimokawa, and Watson tests. The critical values (CV) and power of each test are obtained based on a simulation study by using SRS and RSS methods considering various sample sizes and alternatives. A rain data set is used to investigate the effectiveness of the suggested GFTs. Based on the same number of measured units for the various alternatives taken into consideration in this study, it is discovered that the RSS tests are more effective than those of their rivals in SRS. Additionally, as the set size increases, the GFTs’ power increases.

Efficient Estimation of Two-Parameter Xgamma Distribution Parameters Using Ranked Set Sampling Design

An efficient method such as ranked set sampling is used for estimating the population parameters when the actual observation measurement is expensive and complicated. In this paper, we consider the problem of estimating the two-parameter xgamma (TPXG) distribution parameters under the ranked set sampling as well as the simple random sampling design. Various estimation methods, including the weighted least-square estimator, maximum likelihood estimators, least-square estimator, Cramer–von Mises, the maximum product of spacings estimators, and Anderson–Darling estimators, are considered. A comparison between the ranked set sampling and simple random sampling estimators, with the same number of measurement units, is conducted using a simulation study in terms of the bias, mean squared errors, and efficiency of estimators. The merit of the ranked set sampling estimators is examined using real data of bank customers. The results indicate that estimations using the ranked set sampling method are more efficient than the simple random sampling competitor considered in this study.

Information theory approach to ranked set sampling and new sub-ratio estimators

In this study, we introduce a new approach to the mean estimators in ranked set sampling. The amount of information carried by the auxiliary variable is measured with the Shannon entropy method on populations and samples and to use this information in the estimator, the basic ratio and the generalized exponential ratio estimators are modified as sub-ratio estimators to use only the information on the sample. Without using the required population parameter for ratio estimators, we propose new sub-ratio type estimators using only the auxiliary variable for ranking in the implementation of the ranked set sampling method. The mean squared errors and bias formulas of the proposed estimators are obtained and it is shown that the proposed estimators are more efficient than the classic mean estimator and ratio estimator of RSS under the certain theoretical conditions. Simulation and real data studies also show that the proposed estimators always give better results than the mean estimators of ranked set sampling and it is observed that the relative efficiencies of the proposed estimators increase depending on the magnitude of the entropy, the correlation between the auxiliary and the study variables, and the set sizes.

New Exponential Ratio Estimator in Ranked Set Sampling

In this study, we adapted the families of estimators from Ünal and Kadilar (2021) using the exponential function for the population mean in case of non-response for simple random sampling for the estimation of the mean of the population with the RSS (ranked set sampling) method. The equations for the MSE and the bias of the adapted estimators are obtained for RSS and it in theory shows that the proposed estimator is additional efficient than the present RSS mean estimators in the literature. In addition, we support these theoretical results with real COVID-19 real data and conjointly the simulation studies with different distributions and parameters. As a result of the study, it was observed that the efficiency of the proposed estimator was better than the other estimators.

A Suggestion for Using Ranked Set Sampling in Household Expenditure and Income Survey

The ranked set sampling method uses the ranking information of the units to provide a more representative sample of the population to the survey designers. The sampling distribution is closer to the actual distribution of the population. In this article, to ensure the effectiveness of ranked set sampling in extensive surveys conducted to prepare official statistics, we intend to use this sampling method to improve the efficiency of key estimates of household expenditure and income survey of the Statistics Center of Iran. The results show that using ranked set sampling to design household expenditure and income surveys can improve the efficiency of key estimates of the study, provided that the ranking variable used has a high correlation with the main variables of the study. Obviously, in the absence of a suitable and available variable for ranking the units, the information of the sampling frame can be used to construct a ranking variable correlated with the key variables of the survey.

Reliability Estimation of Inverse Lomax Distribution Using Extreme Ranked Set Sampling

In survival analysis, the two-parameter inverse Lomax distribution is an important lifetime distribution. In this study, the estimation of R = P Y < X is investigated when the stress and strength random variables are independent inverse Lomax distribution. Using the maximum likelihood approach, we obtain the R estimator via simple random sample (SRS), ranked set sampling (RSS), and extreme ranked set sampling (ERSS) methods. Four different estimators are developed under the ERSS framework. Two estimators are obtained when both strength and stress populations have the same set size. The two other estimators are obtained when both strength and stress distributions have dissimilar set sizes. Through a simulation experiment, the suggested estimates are compared to the corresponding under SRS. Also, the reliability estimates via ERSS method are compared to those under RSS scheme. It is found that the reliability estimate based on RSS and ERSS schemes is more efficient than the equivalent using SRS based on the same number of measured units. The reliability estimates based on RSS scheme are more appropriate than the others in most situations. For small even set size, the reliability estimate via ERSS scheme is more efficient than those under RSS and SRS. However, in a few cases, reliability estimates via ERSS method are more accurate than using RSS and SRS schemes.

A New Estimation Study of the Stress-Strength Reliability for the Topp–Leone Distribution Using Advanced Sampling Methods

In this manuscript, we investigate the estimation of the unknown reliability measure R = P [Y < X], in the case where Y and X are two independent random variables with Topp–Leone distributions. As the main contribution, various advanced sampling strategies are studied. The suggested strategies are simple random, ranked set, and median ranked set samplings. Firstly, based on the maximum likelihood, we give an efficient estimator of R when the observations of the two random variables are selected from the same simple random sample. Secondly, such an estimator is addressed when the observations of the two random variables are selected from the ranked set sampling method. Then, based on median ranked set sampling, the maximum likelihood estimator of R is addressed in all the four cases. When the observations from the two random variables are selected from the same set size, two cases are considered, while the other two cases are considered at different set sizes. A simulation research is developed to evaluate the behavior of the obtained estimates based on standard and median ranked set samplings with their simple random sampling equivalents. The ratio of mean square error is used to assess the effectiveness of these estimates.

Efficient Estimation of the Generalized Quasi-Lindley Distribution Parameters under Ranked Set Sampling and Applications

Ranked set sampling is a very useful method to collect data when the actual measurement of the units in a population is difficult or expensive. Recently, the generalized quasi-Lindley distribution is suggested as a new continuous lifetime distribution. In this article, the ranked set sampling method is considered to estimate the parameters of the generalized quasi-Lindley distribution. Several estimation methods are used, including the maximum likelihood, the maximum product of spacings, ordinary least squares, weighted least squares, Cramer–von Mises, and Anderson–Darling methods. The performance of the proposed ranked set sampling based estimators is achieved through a simulation study in terms of bias and mean squared errors compared to the simple random sample. Additional results are obtained based on real data for the survival times of 72 guinea pigs and 23 ball bearings. The simulation study results and the real data applications showed the superiority of the proposed ranked set sampling estimators compared to the simple random sample competitors based on the same number of measuring units.