Robust extreme double ranked set sampling

As a well-known method for selecting representative samples of populations, ranked set sampling (RSS) has been considered increasingly in recent years. This (RSS) method has proved to be more efficient than the usual simple random sampling (SRS) for estimating most of the population parameters. In order to have a more efficient estimate of the population mean, a new sampling scheme called as robust extreme double ranked set sampling (REDRSS) is introduced and investigated in this paper. A simulation study shows that using REDRSS scheme gives more efficient estimates of population mean with smaller variance than the usual SRS, RSS and most other sampling schemes based on RSS estimators in non-uniform (symmetric or non-symmetric) distributions.     

Estimating the population proportion in modified ranked set sampling methods

In this paper, proportion estimators and associated variance estimators are proposed for a binary variable with a concomitant variable based on modified ranked set sampling methods, which are extreme ranked set sampling (ERSS), median ranked set sampling (MRSS), percentile ranked set sampling (Per-RSS) and L ranked set sampling (LRSS) methods. The Monte Carlo simulation study is performed to compare the performance of the estimators based on bias, mean squared error, and relative efficiency for different levels of correlation coefficient, set and cycle sizes under normal and log-normal distributions. Moreover, the study is supported with real data application.     

Improved estimation of scale parameters of morgenstern type bivariate uniform distribution using ranked set sampling

ABSTRACT

In this article we suggest some improved version of estimators of scale parameter of Morgenstern-type bivariate uniform distribution (MTBUD) based on the observations made on the units of the ranked set sampling regarding the study variable Y which is correlated with the auxiliary variable X, when (X, Y) follows a MTBUD. We also suggest some linear shrinkage estimators of scale parameter of Morgenstern type bivariate uniform distribution (MTBUD). Efficiency comparisons are also made in this work.     

The mg-procedure in ranked set sampling

The MG-procedure in ranked set sampling is studied in this paper. It is shown that the MG-procedure with any selective probability matrix provides a more efficient estimator than the sample mean based on simple random sampling. The optimum selective probability matrix in the procedure is obtained and the estimator based on it is shown to be more efficient than that studied by Yanagawa and Shirahata [5]. The median-mean estimator, which is more efficient and could be easier to apply than that proposed by McIntyre [2] and Takahashi and Wakinoto [3], is proposed when the underlying distribution function belongs to a certain subfamily of symmetric distribution functions which includes the normal, logistic and double exponential distributions among others.     

Reliability estimation based on ranked set sampling

In this paper we consider the problem of estimating the reliability of an exponential component based on a Ranked Set Sample (RSS) of size n. Given the first r observations of that sample, 1≤r≤n, we construct an unbiased estimator for this reliability and we show that these n unbiased estimators are the only ones in a certain class of estimators. The variances of some of these estimators are compared. By viewing the observations of the RSS of size n as the lifetimes of n independent k-out-of-n systems, 1≤k≤n, we are able to utilize known properties of these systems in conjunction with the powerful tools of majorization and Schur functions to derive our results.     

Paired double-ranked set sampling

Abstract

In environmental monitoring and assessment, the main focus is to achieve observational economy and to collect data with unbiased, efficient and cost-effective sampling methods. Ranked set sampling (RSS) is one traditional method that is mostly used for accomplishing observational economy. In this article, we propose an unbiased sampling scheme, named paired double RSS (PDRSS) for estimating the population mean. We study the performance of the mean estimators under PDRSS based on perfect and imperfect rankings. It is shown that, for perfect ranking, the variance of the mean estimator under PDRSS is always less than the variance of mean estimator based on simple random sampling, paired RSS and RSS. The mean estimators under RSS, median RSS, PDRSS, and double RSS are also compared with the regression estimator of population mean based on SRS. The procedure is also illustrated with a case study using a real data set.     

Estimating population characteristics by incorporating prior values in stratified random sampling/ranked set sampling

In this paper, we discuss the estimation of population characteristics using stratified random sampling in an infinite population framework, including ranked set sampling as a special case. The use of prior values is considered and the underlying distribution is assumed to be unknown. The estimator considered in each stratum is the weighted mean of the U-statistic and prior value. The optimum weight is obtained by minimizing the mean squared error of the estimator of the population characteristics, but it contains unknown parameters and those parameters are replaced with their estimates. Simulation results show the gains in efficiency of the proposed estimator, yielding gains of at least 1.2 times larger than the usual unbiased estimator under certain condition specified in the text. Guidelines for the usage of the proposed estimator are shown and an application to a real data set is provided.     

Improved best linear unbiased estimators for the simple linear regression model using double ranked set sampling schemes

ABSTRACT

In this paper, we consider the best linear unbiased estimators (BLUEs) based on double ranked set sampling (DRSS) and ordered DRSS (ODRSS) schemes for the simple linear regression model with replicated observations. We assume three symmetric distributions for the random error term, i.e., normal, Laplace and some scale contaminated normal distributions. The proposed BLUEs under DRSS (BLUEs-DRSS) and ODRSS (BLUEs-ODRSS) are compared with the BLUEs based on ordered simple random sampling (OSRS), ranked set sampling (RSS), and ordered RSS (ORSS) schemes. These estimators are compared in terms of relative efficiency (RE), RE of determinant (RED), and RE of trace (RET). It is found that the BLUEs-ODRSS are uniformly better than the BLUEs based on OSRS, RSS, ORSS, and DRSS schemes. We also compare the estimators based on imperfect RSS (IRSS) schemes. It is worth mentioning here that the BLUEs under ordered imperfect DRSS (OIDRSS) are better than their counterparts based on IRSS, ordered IRSS (OIRSS), and imperfect DRSS (IDRSS) methods. Moreover, for sensitivity analysis of the BLUEs, we calculate REs and REDs of the BLUEs under the assumption of normality when in fact the parent distribution follows a non normal symmetric distribution. It turns out that even under violation of normality assumptions, BLUEs of the intercept and the slope parameters are found to be unbiased with equal REs under each sampling scheme. It is also observed that the BLUEs under ODRSS are more efficient than the existing BLUEs.     

Partial groups ranked set sampling and mean estimation

Ranked set sampling (RSS) is an advanced sampling method which is very effective for estimating mean of the population when exact measurement of observation is difficult and/or expensive. Balanced Groups RSS (BGRSS) is one of the modification of RSS where only the lowest, the median and the largest ranked units are taken into account. Although BGRSS is advantageous and useful for some specific cases, it has strict restrictions regarding the set size which could be problematic for sampling plans. In this study, we make an improvement on BGRSS and propose a new design called Partial Groups RSS which offers a more flexible sampling plan providing the independence of the set size and sample size. Partial Groups RSS also has a cost advantage over BGRSS. We construct a Monte Carlo simulation study comparing the performance of the mean estimators of the proposed sampling design and BGRSS according to their sampling costs and mean squared errors for various type of distributions. In addition, we give a biometric data application for investigating the efficiency of Partial Groups RSS in real life applications.     

Estimation of the distribution function under hybrid ranked set sampling

Recently, a hybrid ranked set sampling (HRSS) scheme has been proposed in the literature. The HRSS scheme encompasses several existing ranked set sampling (RSS) schemes, and it is a cost-effective alternative to the classical RSS and double RSS schemes. In this paper, we propose an improved estimator for estimating the cumulative distribution function (CDF) using HRSS. It is shown, both theoretically and numerically, that the CDF estimator under HRSS scheme is unbiased and its variance is always less than the variance of the CDF estimator with simple random sampling (SRS). An unbiased estimator of the variance of CDF estimator using HRSS is also derived. Using Monte Carlo simulations, we also study the performances of the proposed and existing CDF estimators under both perfect and imperfect rankings. It turns out that the proposed CDF estimator is by far a superior alternative to the existing CDF estimators with SRS, RSS and L-RSS schemes. For a practical application, a real data set is considered on the bilirubin level of babies in neonatal intensive care.     

Concomitant record ranked set sampling

In this work, we define a new method of ranked set sampling (RSS) which is suitable when the characteristic (variable) Y of primary interest on the units is jointly distributed with an auxiliary characteristic X on which one can take its measurement on any number of units, so that units having record values on X alone are ranked and retained for making measurement on Y. We name this RSS as concomitant record ranked set sampling (CRRSS). We propose estimators of the parameters associated with the variable Y of primary interest based on observations of the proposed CRRSS which are applicable to a very large class of distributions viz. Morgenstern family of distributions. We illustrate the application of CRRSS and our estimation technique of parameters, when the basic distribution is Morgenstern-type bivariate logistic distribution. A primary data collected by CRRSS method is demonstrated and the obtained data used to illustrate the results developed in this work.     

An application of ranked set sampling when observations from several distributions are to be included in the sample

ABSTRACT

In this article, we propose a method to estimate the common location and common scale parameters of several distributions using suitably defined ranked set sampling. Efficiency comparison of the obtained estimators with some of the standard estimators is made. Illustration of the results to real life data sets is also described.     

On extropy properties of ranked set sampling

Ranked set sampling is a sampling design that allows the experimenter to span the full range values in the population and it can be used widely in industrial, environmental and ecological studies. In this paper, we consider the information content of ranked set sampling in terms of extropy measure. It is shown that the ranked set sampling performs better than its simple random sample counterpart of the same size. Monotone properties and stochastic orders are investigated. Sharp bounds on the extropy of RSS data based on the projection method in the non-parametric set-up as well as Steffensen inequalities in the parametric context are established. The extropy measure can also be used as a discrimination tool between RSS and SRS data.     

Estimation of bivariate characteristics using ranked set sampling

The superiority of ranked set sampling (RSS) over simple random sampling (SRS) for estimating the mean of a population is well known. This paper introduces and investigates a bivariate version of RSS for estimating the means of two characteristics simultaneously. It turns out that this technique is always superior to SRS and the usual univariate RSS of the same size. The performance of this procedure for a specific distribution can be evaluated using simulation or numerical computation. For the bivariate normal distribution, the efficiency of the procedure with respect to that of SRS is evaluated exactly for set size m = 2 and 3. The paper shows that the proposed estimator is more efficient than the regression RSS estimators proposed by Yu & Lam (1997) and Chen (2001). Real data that consist of heights and diameters of 399 trees are used to illustrate the procedure. The procedure can be generalized to the case of multiple characteristics.     

Performance of coefficient of variation estimators in ranked set sampling

In this paper, we propose and evaluate the performance of different parametric and nonparametric estimators for the population coefficient of variation considering Ranked Set Sampling (RSS) under normal distribution. The performance of the proposed estimators was assessed based on the bias and relative efficiency provided by a Monte Carlo simulation study. An application in anthropometric measurements data from a human population is also presented. The results showed that the proposed estimators via RSS present an expressively lower mean squared error when compared to the usual estimator, obtained via Simple Random Sampling. Also, it was verified the superiority of the maximum likelihood estimator, given the necessary assumptions of normality and perfect ranking are met.     

Bayesian inference and prediction of the Pareto distribution based on ordered ranked set sampling

In this paper, order statistics from independent and non identically distributed random variables is used to obtain ordered ranked set sampling (ORSS). Bayesian inference of unknown parameters under a squared error loss function of the Pareto distribution is determined. We compute the minimum posterior expected loss (the posterior risk) of the derived estimates and compare them with those based on the corresponding simple random sample (SRS) to assess the efficiency of the obtained estimates. Two-sample Bayesian prediction for future observations is introduced by using SRS and ORSS for one- and m-cycle. A simulation study and real data are applied to show the proposed results.     

Estimation of the parameters of Downton's bivariate exponential distribution using ranked set sampling scheme

The parameters of Downton's bivariate exponential distribution are estimated based on a ranked set sample. Parametric and nonparametric methods are considered. The suggested estimators are compared to the corresponding ones based on simple random sampling. It turns out that some of the suggested estimators are significantly more efficient than the ones based on simple random sampling.     

Estimation of system reliability for exponential distributions based on L ranked set sampling

Abstract

In the case where strength and stress both follow exponential distributions, this paper considers the maximum likelihood estimator (MLE) of the system reliability based on L ranked set sampling (LRSS). The proposed MLE is shown to have existence, uniqueness and asymptotic normality, and its asymptotic variance is obtained by the Fisher information matrix of LRSS. The values of asymptotic relative efficiencies show that the proposed MLE is always more efficient than the MLE using simple random sampling (SRS). However, the MLE using LRSS cannot be written in closed form. Therefore, the modified MLE is proposed using the technique replaced some terms in the maximum likelihood equations by their expectations. The newly modified MLE using LRSS is shown to be superior to the MLE using SRS. Finally, the proposed method is applied to a real data set on metastatic renal carcinoma study.     

Two-stage cluster sampling with hybrid ranked set sampling in the secondary sampling frame

In surveys of natural resources in agriculture, ecology, fisheries, forestry, environmental management, etc., cost-effective sampling methods are of major concern. In this paper, we propose a two-stage cluster sampling (TSCS) in integration with the hybrid ranked set sampling (HRSS)—named TSCS-HRSS—in the second stage of sampling for estimating the population mean. The TSCS-HRSS scheme encompasses several existing ranked set sampling (RSS) schemes and may help in selecting a smaller number of units to rank. It is shown both theoretically and numerically that the TSCS-HRSS provides an unbiased estimator of the population mean and it is more precise than the mean estimators based on TSCS with SRS and RSS schemes. An unbiased estimator of the variance of the proposed mean estimator is also derived. A similar trend is observed when studying the impact of imperfect rankings on the performance of the TSCS-HRSS based mean estimator.     

Sign test for ranked-set sampling

The exact null distribution of the ranked-set sample (RSS) sign test statistic is computed. The power of this test is compared with the simple random sample (SRS) sign test for some continuous symmetric distributions. The problem of imperfect judgement is discussed. The superiority of RSS over SRS is demonstrated.