Ranked Set Sampling Research Articles

Reliability Estimation in Multicomponent Stress-Strength for Generalized Inverted Exponential Distribution Based on Ranked Set Sampling

Stress-strength models are considered of great significance due to their applicability in varied fields. We address the estimation of the system reliability of a multicomponent stress-strength model, say Rs,k, of an s out of k system when the pair stress and strengths are drawn from a generalized inverted exponential distribution. The system is deemed as working if at least s out of k strengths be more than its stress. We obtain the reliability estimators when the data of strength and stress distributions are collected from three sampling schemes, specifically; simple random sampling, ranked set sampling, and median ranked set sampling. We obtain four estimators of Rs,k out from median ranked set sampling. The behavior of different estimates is examined via a simulation study based on mean squared errors and efficiencies. The simulation studies point out that the reliability estimates of Rs,k, from the ranked set sampling scheme are preferred than other estimates picked from the simple random sample and median ranked set sampling in a majority of the situations. The theoretical studies are explained with the aid of real data analysis.

Optimum stratification for equal allocation using ranked set sampling as a method of selection

Present investigation deals with the problem of optimum stratification on the auxiliary variable for equal allocation when method of selection of units in individual strata is done by ranked set sampling (RSS). A rule of obtaining approximate optimum strata boundaries has been developed by minimizing the variance and solution of minimal equations thereof. A numerical analysis on the basis of percent relative efficiency has also been made, which indicated remarkable gain in efficiency.

Interval Estimation of the Stress-Strength Reliability for Lower Record Data Based on One-parameter Exponential Distribution Using Median Ranked Set Sampling and Record Ranked Set Sampling

This paper develops interval estimation of stress-strength reliability when data are lower record values from a one-parameter exponential distribution using resampling schemes such as median ranked set sampling (MRSS) and record ranked set sampling (RRSS). For illustrative aims, we inspect the performance of the proposed interval estimation methods, bootstrap, and generalized confidence intervals (CIs) by using a simulation study and real examples. The result indicates that the proposed interval based on a bootstrap percentile (BP) CI and a generalized CI (GC) using MRSS is suitable for the application.

Inference on P(Y < X) Based on Ranked Set Sample for Generalized Pareto Distribution

Inference on P(Y < X) Based on Ranked Set Sample for Generalized Pareto Distribution

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

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.

New mixed ranked set sampling variations

Building efficient sampling procedures to provide more accurate results with small sample sizes is one of the main goals in sampling surveys. The ranked set sampling (RSS) is a well‐known procedure for selecting representative samples and improving parametric estimation by employing ranking on observations. In order to have a more efficient sampling procedure, new sampling procedures are proposed and investigated in this article. The main focus of this article is to enhance the mean estimation of the study population using the proposed RSS procedures. The performance of the proposed sampling procedures is compared with their competitors in RSS, double RSS (DRSS), extreme RSS (ERSS), and double extreme RSS (DERSS) by conducting simulation studies for numerous (symmetric and asymmetric) distributions. An application to a real dataset is also considered to exemplify the achievement of the proposals. Numerical simulations show that the new modified estimators are unbiased for the population mean for symmetric distributions and they outperform their competitors in most of the cases investigated in this article.

Estimating the Reliability Function for Transmuted Pareto Distribution Using Simulation

In this work, the methods (Moments, Modified Moments, L-Moments, Percentile, Rank Set sampling and Maximum Likelihood) were used to estimate the reliability function and the two parameters of the Transmuted Pareto (TP) distribution. We use simulation to generate the required data from three cases this indicates sample size , and it replicates for the real value for parameters, for reliability times values we take .&#x0D; Results were compared by using mean square error (MSE), the result appears as follows :&#x0D; The best methods are Modified Moments, Maximum likelihood and L-Moments in first case, second case and third case respectively.

Exact prediction intervals for future exponential and Pareto lifetimes based on ordered ranked set sampling of non-random and random size

In the present paper, two pivotal statistics are suggested to construct prediction intervals of future observations from the exponential and Pareto distributions in the context of ordered ranked set sample. Our study encompasses two cases. The first case, when the sample size is assumed to be fixed and the second case when the sample size is assumed to be a positive integer-valued random variable. In addition to deriving explicit forms for the distribution functions of the two pivotal statistics, we consider some special cases for the random size of the sample. Moreover, a simulation study is carried out to assess the efficiency of the suggested methods. Finally, an example representing lifetime data is analyzed.

New insights on goodness-of-fit tests for ranked set samples

New insights on goodness-of-fit tests for ranked set samples

Fisher information in ranked set sampling from the simple linear regression model

Fisher information is a fundamental concept of statistical inference and plays an important role in many areas of statistical analysis. In this paper, we obtain explicit expressions for the Fisher information matrix in ranked set sampling (RSS) from the simple linear regression model with replicated observations. It has been shown to be the sum of two matrices, one of which is the Fisher information matrix based on simple random sampling (SRS). The numerical results show that RSS provides more information than SRS when the same sample size is used.

Using a rank-based design in estimating prevalence of breast cancer

It is highly important for governments and health organizations to monitor the prevalence of breast cancer as a leading source of cancer-related death among women. However, the accurate diagnosis of this disease is expensive, especially in developing countries. This article concerns a cost-efficient method for estimating prevalence of breast cancer, when diagnosis is based on a comprehensive biopsy procedure. Multistage ranked set sampling (MSRSS) is utilized to develop a proportion estimator. This design employs imprecise rankings based on some visually assessed cytological covariates, so as to provide the experimenter with a more informative sample. Theoretical properties of the proposed estimator are explored. Evidence from numerical studies is reported. The developed procedure can be substantially more efficient than its competitor in simple random sampling (SRS). In some situations, the proportion estimation in MSRSS needs around 76% fewer observations than that in SRS, given a precision level. Thus, using MSRSS may lead to a considerable reduction in cost with respect to SRS. In many medical studies, e.g., diagnosing breast cancer based on a full biopsy procedure, exact quantification is difficult (costly and/or time-consuming), but the potential sample units can be ranked fairly accurately without actual measurements. In this setup, multistage ranked set sampling is an appropriate design for developing cost-efficient statistical methods.

Improved confidence intervals based on ranked set sampling designs within a parametric bootstrap approach

Improved confidence intervals based on ranked set sampling designs within a parametric bootstrap approach

An efficient class of estimators based on ranked set sampling

An efficient class of estimators based on ranked set sampling

On distribution selection under ranked set sampling schemes

Distribution selection plays a key role in parametric statistics. Choosing one from a set of candidate distributions that best fits the sample data is a recurring task in a large number of statistical analysis. The choice of a misspecified and/or poor fitted distribution can lead to unreliable results and conclusions. Although distribution selection has been widely studied regarding goodness of fit procedures, less attention has been given on how the sampling design impacts the chance of choosing the most suitable distribution. In this work we address the performance of ranked set sampling (RSS), extreme ranked set sampling (ERSS), and mixture ranked set sampling (MRSS) in distribution selection. In particular, we focus on count data, an important and very usual class of random variables. A comprehensive simulation study was carried out, accounting for five distributions: Poisson, negative binomial, geometric, zero-inflated Poisson, and zero-inflated negative binomial. Results show that RSS and extensions performed better than simple random sampling (SRS) under perfect ranking. When ranking errors are present, better efficiency depends on how accurate is the ranking criterion, and the different RSS-based designs also differ in terms of their robustness. Findings are reinforced by additional simulation based on two real data sets.

Parameter Estimation Based on Double Ranked Set Samples with Applications to Weibull Distribution

In this paper, the likelihood function for parameter estimation based on double ranked set sampling (DRSS) schemes is introduced. The proposed likelihood function is used for the estimation of the Weibull distribution parameters. The maximum likelihood estimators (MLEs) are investigated and compared to the corresponding ones based on simple random sampling (SRS) and ranked set sampling (RSS) schemes. A Monte Carlo simulation is conducted and the absolute relative biases, mean square errors, and efficiencies are compared for the different schemes. It is found that, the MLEs based on DRSS is more efficient than MLE using SRS and RSS for estimating the two parameters of the Weibull distribution (WD).

Generalized Chain Regression-cum-Chain Ratio Estimator for Population Mean under Stratified Extreme-cum-Median Ranked Set Sampling

Estimation of population mean of study variable Y suffers loss of precision in the presence of high variation in the data set. The use of auxiliary information incorporated in construction of an estimator under ranked set sampling scheme results in efficient estimation of population mean. In this paper, we propose an efficient generalized chain regression-cum-chain ratio type estimator to estimate finite population mean of study variable under stratified extreme-cum-median ranked set sampling utilizing information on two auxiliary variables. Mean square error (MSE) of the proposed generalized estimator is derived up to first order of approximation. The applications of the proposed estimator under symmetrical and asymmetrical probability distributions are discussed using simulation study and real-life data set for comparisons of efficiency. It is concluded that the proposed generalized estimator performs efficiently as compared to some existing estimators. It is also observed that the efficiency of the proposed estimator is directly proportional to the correlations between the study variable and its auxiliary variables.

CUM DUAL PRODUCT ESTIMATOR FOR THE POPULATION MEAN USING RANKED SET SAMPLING

It has been shown that Ranked Set Sampling (RSS) is highly beneficial to the estimation based on Simple Random Sampling (SRS). There has been considerable development and many modifications were done to this method. The problem of estimating the population means is an integral aspect of a scientific survey. The estimators were examined for cum-dual products under Ranked Set Sampling (RSS), while the first-order approximation to the bias and Mean Square Error (MSE) of the proposed estimators were obtained. The numerical illustration of the comparisons was carried out to support the claim that the proposed estimators are more efficient than some existing estimators. Data were simulated for study variable y and auxiliary variable x using R software for the analysis to support the claim. The result shows that MSE of the proposed estimators, y ̅_(pd,RSS)^* is smaller than the MSE of the existing estimators y ̅_pd^*,y ̅_Rd^*, y ̅_(R,RSS)^*,y ̅_(RSS,MM1)^* and y ̅_(RSS,MM2)^* and y ̅_(RSS,MM3)^* at ρ = −0.1,−0.2,0.1,0.2, hence, the proposed estimator performed better than the existing estimators. While the MSE of the proposed estimator yy ̅_(pd,RSS)^* is greater than the MSE of the existing estimators y ̅_pd^* and y ̅_Rd^* at ρ = -0.3 and 0.3. However, the proposed estimator y ̅_(pd,RSS)^* does not perform better than the estimators, y ̅_pd^*,and y ̅_Rd^* at ρ = -0.3 and 0.3. It was concluded that the proposed estimator was more efficient than a class of regression estimators and four existing ratio-type estimators based on RSS.

On Extended Neoteric Ranked Set Sampling Plan: Likelihood Function Derivation and Parameter Estimation

The 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. Therefore, 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. These modifications include the extended ranked set sampling (ERSS) plan and the neoteric ranked set sampling (NRSS) plan. The results as foreseeable were very satisfactory and gave similar results to Taconeli and Cabral’s 2019 results.

A modified regression-cum-ratio estimator for finite population mean in presence of nonresponse using ranked set sampling

&lt;abstract&gt; &lt;p&gt;Several situations arise where decision-making is required for some characteristics of an asymmetrical population for example estimation of the weekly number of server breakdowns at a company. The estimation methods based upon classical sampling designs are not suitable in such situations and some specialized methods and/or estimators are required. The ranked set sampling is a procedure that is suitable in such situations. In this paper, a new estimator is proposed that can be used to estimate population characteristics in case of asymmetrical populations. The proposed estimator is useful for estimation of population mean in the presence of non-response in study variable by using ranked set sampling procedure. The estimator is based upon two auxiliary variables to reduce the effect of asymmetry. The use of two auxiliary variables is also helpful in minimizing the variation in the estimation of the population mean of the study variable. The ranked set sampling procedure is used to get better accuracy as the actual measurements may be time-consuming, expensive, or difficult to obtain in a small sample size. The use of ranked set sampling also reduces the effect of asymmetry in the characteristics under study. The expressions for the mean square error and bias for the proposed estimators have been derived. The performance of the proposed estimator is evaluated by using real-life data and a simulation study is carried out to get an overview of efficiency. The relative efficiency of the proposed estimator is compared with some existing estimators. It has been found that the proposed estimator is highly efficient as compared with Mohanty's regression cum ratio estimator in simple random sampling and is more reliable in the case of non-response with a small sample size.&lt;/p&gt; &lt;/abstract&gt;

Approximate Optimum Strata Boundaries for Equal Allocation under Ranked Set Sampling

Optimum stratification is the method of choosing the best boundaries that make strata internally homogeneous, given some sample allocation. In order to make the strata internally homogenous, the strata should be constructed in such a way that the strata variances for the characteristic under study be as small as possible. This could be achieved effectively by having the distribution of the study variable known and create strata by cutting the range of the distribution at suitable points. If the frequency distribution of the study variable is unknown, it may be approximated from the past experience or some prior knowledge (auxiliary information) obtained at a recent study. In this study, problem of optimum stratification on the auxiliary variable x for equal allocation has been considered. A ( ) 3 cum K x rule of obtaining approximately optimum strata boundaries has been proposed under ranked set sampling. A numerical investigation with relative efficiency has also been made.