Extreme Ranked Set Sampling Research Articles

Location charts based on concomitants of ranked set samples from Morgenstern family

This paper surveys the location chart based on concomitants of ranked set sampling (RSS), a triangular modification of RSS, which is known as maximum ranked set sampling with unequal sample (MRSSU) and the extreme ranked set sampling (ERSS) from the Farlie–Gumbel–Morgenstern bivariate family. We also remarked both heavy-tailed symmetric and skewed distributions throughout the paper. For the performance evaluation of the charts, extensive utilization of the Monte Carlo simulations is carried out using average run length (ARL), extra quadratic loss (EQL), relative ARL (RARL), and performance comparison index (PCI) measures, and finally, conclusion ends this research.

On the improvement of paired ranked set sampling to estimate population mean

Abstract In ecological and environmental sampling the quantification of units is either difficult or overly demanding in terms of the time, money, workload, it requires. For this reason efficient and cost-effective sampling methods need to be devised for data collecting. The most commonly used method for this purpose is the Ranked Set Sampling (RSS). In this paper, a sampling scheme called Improved Paired Ranked Set Sampling (IPRSS) is proposed to estimate the population mean. The performance of the proposed IPRSS is evaluated under perfect and imperfect rankings. A simulation study based on selected hypothetical distributions and a real-life data set showed that IPRSS is more precise than RSS, Paired RSS (PRSS) or Extreme RSS (ERSS).

Bayesian Estimation of Morgenstern Type Bivariate Rayleigh Distribution Using Some Types of Ranked Set Sampling

In this paper we consider Bayesian estimation based on bivariate ranked set sample, in which units are ranked based on measurements made on an easily and exactly measurable auxiliary variable X which is correlated with the study variable Y. We obtain Bayes estimator for the scale parameter of the study variate Y, when (X, Y ) follows a Morgenstern type bivariate Rayleigh distribution. The Bayes estimators are considered based on bivari-ate ranked set sampling, extreme ranked set sampling and maximum ranked set sampling with unequal sample. The accuracy of estimation methods in this paper is illustrated using simulation study. Finally, a real data set is analyzed.

Correction to: Log-logistic parameters estimation using moving extremes ranked set sampling design

Correction to: Log-logistic parameters estimation using moving extremes ranked set sampling design

Parametric estimation for the simple linear regression model under moving extremes ranked set sampling design

Parametric estimation for the simple linear regression model under moving extremes ranked set sampling design

Memory type ratio and product estimators under ranked-based sampling schemes

The exponential weighted moving average (EWMA) statistic is utilized the past information along with the present to enhance the efficiency of the estimators used for estimating the population parameters. In this study, the EWMA statistic is used for the estimation of population mean with suitable auxiliary information. The memory type ratio and product estimators are proposed under ranked-based sampling (RBS) schemes including extreme ranked set sampling, median ranked set sampling, and quartile ranked set sampling. The expressions of mean square errors (MSE) of the proposed estimators are derived. An extensive simulation study is conducted to evaluate the performance of the proposed estimators. An empirical study is presented based on real-life data that supports the findings of the simulation study.

Fisher Information in Moving Extreme Ranked Set Sampling with Application to Parameter Estimation

In statistical parameter estimation problems, how well the parameters are estimated largely depends on the sampling design used. In the current paper, a modification of ranked set sampling called moving extremes ranked set sampling (MERSS) is considered for the Fisher information matrix for the location-scale family. The Fisher information matrix for this model are respectively derived under simple random sampling and MERSS. In order to give more insight into the performance of MERSS with respect to simple random sampling, the Fisher information matrix for usual location-scale distributions are respectively computed under the two sampling. The numerical results show that MERSS provides more information than simple random sampling in parametric inference.

Ranked set sampling with lowest order statistics for Pareto distribution

Ranked set sampling (RSS) is a method of sampling that can be advantageous when quantification of all sampling units is costly but when small sets of units can be ranked according to the character under investigation by means of visual inspection or other methods not requiring actual measurements. RSS performs better than simple random sampling (SRS) to estimate the population mean. In original RSS procedure, the units corresponding to each rank are used. In this article, we propose to use RSS method with lowest order statistics from each sample to estimate the population mean of Pareto distribution which is highly positively skew. The Pareto distribution is chosen due to its application in social and scientific phenomenon including the distribution of wealth in a society. The estimator based on lowest order statistics with bias correction term has been proposed. Two cases, known and unknown scale parameter, have been considered. The simulation-based methods have also been included. It is shown that the gains in the relative precisions of population mean based on our proposed method are uniformly higher than those based upon the RSS and extreme RSS procedures. The proposed method with bias correction term is recommended for real applications.

The Efficiency Comparison and Application of Proposed Rhombus Ranked Set Sampling

A new scheme ‘Rhombus Ranked Set Sampling’ (RRSS) is developed in this research together with its properties for estimating the population means. Mathematical validation along with the simulation evaluation is presented. The proposed method is an addition to the family of different sampling methods and generalization of ‘Folded Ranked Set Sampling’ (FRSS). For the simulation process, nine probability distributions are considered for the efficiency comparison of proposed scheme from which four are symmetric and rest are asymmetric among which Weibull and beta distributions which are used twice, unlike parametric values. (Al-Naseer, 2007 and Bani-Mustafa, 2011). Through simulation processes, it is observed that RRSS is competent and more reliable relative to simple random sampling (SRS), ranked set sampling (RSS) and folded ranked set sampling (FRSS). It is noted that for all the underlying distributions, an increase in the efficiency of Rhombus Ranked Set Sampling (RRSS) is achieved via increasing the size of the sample ‘p’. Besides the efficiency comparison, consistency of the proposed method is also valued by using Co-efficient of Variation (CV). Secondary data on zinc (Zn) concentration and lead (Pb) contamination in different parts and tissues of freshwater fish was collected to illustrate the evaluation of RRSS against SRS, RSS, FRSS and ERSS (extreme ranked set sampling). The results obtained through real life illustration defend the simulation study and hence indicates that the RRSS estimator is efficient substitute for existing methods (Al-Omari, 2011).

Log-logistic parameters estimation using moving extremes ranked set sampling design

In statistical parameter estimation problems, how well the parameters are estimated largely depends on the sampling design used. In the current paper, a modification of ranked set sampling (RSS) called moving extremes RSS (MERSS) is considered for the estimation of the scale and shape parameters for the log-logistic distribution. Several traditional estimators and ad hoc estimators will be studied under MERSS. The estimators under MERSS are compared to the corresponding ones under SRS. The simulation results show that the estimators under MERSS are significantly more efficient than the ones under SRS.

Estimation of the distribution function using moving extreme and MiniMax ranked set sampling

Recently, MiniMax ranked set sampling (MiniMax RSS) scheme is suggested for population mean estimation. In this article, we consider moving extreme ranked set sampling (MERSS) and MiniMax RSS for estimating the distribution function of a random variable. Using the maximum likelihood estimation method, new estimators of the cumulative distribution function (CDF) are derived and also their variances are obtained. In the light of a simulation study, we conclude that the estimators based on MiniMax RSS work well compared to those based on MERSS setups regardless of the ranking quality. Additionally, the proposed concomitant-based CDF estimators tend to be superior to their analogs as long as the ranking process is done with fairly good accuracy. For the sake of illustration, two empirical datasets are considered to show the applicability of the proposed estimators in practice.

RATIO ESTIMATION OF THE POPULATION MEAN USING AUXILIARY INFORMATION UNDER THE OPTIMAL SAMPLING DESIGN

Cost-effective sampling design is a problem of major concern in some experiments especially when the measurement of the characteristic of interest is costly or painful or time-consuming. In this article, we investigate ratio-type estimators of the population mean of the study variable, involving either the first or the third quartile of the auxiliary variable, using ranked set sampling (RSS) and extreme ranked set sampling (ERSS) schemes. The properties of the estimators are obtained. The estimators in RSS and ERSS are compared to their counterparts in simple random sampling (SRS) for normal data. The numerical results show that the estimators in RSS and ERSS are significantly more efficient than their counterparts in SRS.

Log-extended exponential-geometric parameters estimation using simple random sampling and moving extremes ranked set sampling

In this paper, estimation of parameters α and β for the log-extended exponential-geometric distribution will be respectively considered in cases when β is known and when both are unknown. Simple random sampling (SRS) and moving extremes ranked set sampling (MERSS) will be used, and several traditional estimators will be considered. The estimators using MERSS are compared to the corresponding ones using SRS. The numerical results show that the estimators using MERSS are significantly more efficient than the ones using SRS. A real data set is used for illustration.

Efficient monitoring of coefficient of variation with an application to chemical reactor process

AbstractControl chart is a useful tool to monitor the performance of the industrial or production processes. Control charts are mostly adopted to detect unfavorable variations in process location (mean) and dispersion (standard deviation) parameters. In the literature, many control charts are designed for the monitoring of process variability under the assumption that the process mean is constant over time and the standard deviation is independent of the mean. However, for many real‐life processes, the standard deviation may be proportional to mean, and hence it is more appropriate to monitor the process coefficient of variation (CV). In this study, we are proposing a design structure of the Shewhart type CV control chart under neoteric ranked set sampling with an aim to improve the detection ability of the usual CV chart. A comprehensive simulation study is conducted to evaluate the performance of the proposed chart in terms of , and measures. Moreover, the comparison of chart is made with the existing competitive charts, based on simple random sampling, ranked set sampling (RSS), median RSS, and extreme RSS schemes. The results revealed that the proposed chart has better detection ability as compared to all existing competitive charts. Finally, a real‐life example is presented to illustrate the working of the newly proposed CV chart.

Modified Extreme Ranked Sets Sampling with Auxiliary Variable

In this paper, a modified extreme ranked set sampling (MERSS) scheme is presented. The ratio estimator under the modified scheme is discussed, and expression of mean square error is derived. The performance of the ratio estimator under MERSS is compared with simple random sampling (SRS), ranked set sampling (RSS), median ranked set sampling (MRSS), quartile ranked set sampling (QRSS) and extreme ranked set sampling (ERSS). A simulation study is conducted, and the results showed that MERSS provides the efficient results as compared to SRS, RSS, MRSS, QRSS and ERSS.

Testing skew-symmetry based on extreme ranked set sampling

The problem of testing skew-symmetry of a distribution is studied in a general model of skew distributions. Toward this end, an order statistic-based test is first introduced to test the null hypotheses of symmetry against the alternative of skew-symmetry of a distribution. Some properties of this test are also studied. Then, using the idea of ranked set sampling, some appropriate sampling schemes are used to test skew-symmetry of a given data set. The power of the proposed tests are compared numerically to determine the best ranked set sampling scheme in different situations. Further, a comparison with some of existing non-parametric tests has been done. A real data set is also used to illustrate the results of the paper. Finally, some conclusions are stated.

Efficient estimation of cumulative distribution function using moving extreme ranked set sampling with application to reliability

In this article, we consider the problem of estimating cumulative distribution function (CDF) and a reliability parameter using moving extreme ranked set sampling (MERSS). Two different CDF estimators are described and compared with their competitors in simple random sampling (SRS) and ranked set sampling (RSS). It turns out the CDF estimators in MERSS can be more efficient than their competitors in SRS and RSS at a point in a particular tail of the distribution when the quality of rankings is sufficiently good. Motivated by this efficiency gain, we develop some estimators for the stress-strength probability using MERSS. The suggested estimators are then compared with their counterparts in the literature via Monte Carlo simulation. Finally, a real dataset is used to show the applicability of the developed procedures.

Permutation Tests for Two-sample Location Problem Under Extreme Ranked Set Sampling

In this paper, permutation test of comparing two-independent samples is investigated in the context of extreme ranked set sampling (ERSS). Three test statistics are proposed. The statistical power of these new test statistics are evaluated numerically. The results are compared with the statistical power of the classical independent two-sample $t$-test, Mann-Whitney $U$ test, and the usual two-sample permutation test under simple random sampling (SRS). In addition, the method of computing a confidence interval for the two-sample permutation problem under ERSS is explained. The performance of this method is compared with the intervals obtained by SRS and Mann-Whitney procedures in terms of empirical coverage probability and expected length. The comparison shows that the proposed statistics outperform their counterparts. Finally, the application of the proposed statistics is illustrated using a real life example.

Maximum likelihood estimation based on ranked set sampling designs for two extensions of the Lindley distribution with uncensored and right-censored data

Ranked set sampling (RSS) has been proved to be a cost-efficient alternative to simple random sampling (SRS). However, there are situations where some measurements are censored, which may not ensure the superiority of RSS over SRS. In this paper, the performance of the maximum likelihood estimators is examined when the data are assumed to follow a Power Lindley or a Weighted Lindley distribution, and are collected according to the original RSS or one of its two variations (the median and extreme RSS). An extensive simulation study, considering uncensored and right-censored data, and perfect and imperfect ranking, is carried out based on the two mentioned distributions in order to compare the performance of the maximum likelihood estimators from RSS-based designs with the corresponding SRS estimators. Two illustrations are presented based on real data sets. The first involves the lifetimes of aluminum specimens, while the second deals with the amount of spray mixture deposited on the leaves of apple trees.

Further Improving the Performance of Logistic Regression Analysis Using Double Extreme Ranking

For dichotomous or ordinal dependent variables, logistic regression models as one of the generalized linear models have been intensively applied in several fields. We proposed a more powerful performance of logistic regression model analysis when a modified extreme ranked set sampling (modified ERSS) is used and further improved the performance when a modified double extreme ranked set sampling (modified DERSS) is used. We assume that ranking could be performed based on an available and easy-to-rank auxiliary variable, which is associated with the response variable. Theoretically and by simulations, we showed the superiority of the performance of the logistic regression analysis when ERSS and DERSS are used compared with using the simple random sample. We illustrated the procedures developed using real data from the 2011/12 National Survey of Children’s Health.