Ranked Set Sampling Procedure Research Articles

Weighted Ranked Set Sampling for Skewed Distributions

Ranked set sampling (RSS) is a useful technique for improving the estimator of a population mean when the sampling units in a study can be more easily ranked than the actual measurement. RSS performs better than simple random sampling (SRS) when the mean of units corresponding to each rank is used. The performance of RSS can be increased further by assigning weights to the ranked observations. In this paper, we propose weighted RSS procedures to estimate the population mean of positively skewed distributions. It is shown that the gains in the relative precisions of the population mean for chosen distributions are uniformly higher than those based on RSS. The gains in relative precisions are substantially high. Further, the relative precisions of our estimator are slightly higher than the ones based on Neyman’s optimal allocation model for small sample sizes. Moreover, it is shown that the performance of the proposed estimator increases as the skewness increases by using the example of the lognormal family of distributions.

Inference for a general family of exponentiated distributions under ranked set sampling with partially observed complementary competing risks data

ABSTRACT Ranked set sampling (RSS) acts as an efficient way for collecting failure information due to its ability of saving testing time and cost, and this paper discusses statistical inference for complementary competing risks model under a modified RSS scheme called the maximum ranked set sampling procedure with unequal samples (MRSSU). When the lifetimes of causes of failure are characterized by a general family of exponentiated distributions with partially observed failure causes, parameter estimation is explored from classical likelihood and Bayesian approaches. Existence and uniqueness of maximum likelihood estimators for model parameters are established, and approximate confidence intervals are constructed in consequence. With respect to general flexible priors, Bayes point and interval estimates are constructed, and associated Monte-Carlo sampling is proposed for complex posterior computation. In addition, when there is extra restriction information available, likelihood and Bayes estimates are also proposed in this regard. Extensive simulation studies are conducted to investigate the performance of different methods, and a real-life example is carried out to demonstrate the applications of our results.

Designing efficient dispersion control charts under various ranked-set sampling approaches

This study presents an in-depth evaluation of fourteen distinct ranked-set sampling methodologies employed to enhance the efficacy of Shewhart-type dispersion charts in identifying persistent shifts in underlying industrial processes. Despite the widespread use of Shewhart-type control charts under simple random sampling for monitoring process dispersion parameters, the efficiency of these dispersion charts under ranked-set sampling procedures has been largely overlooked. Through comprehensive simulation exercises, we obtained the run-length characteristics of the proposed charts, thereby laying a foundation for the comparative analysis of different sampling strategies. Our findings emphasize the superior performance of modified neoteric ranked-set sampling, which consistently outperformed the other techniques in all tested scenarios. Furthermore, we included an example to reinforce the significance and utility of the proposed methodologies in real-world industrial settings. This study provides additional results for optimal statistical control processes, highlighting the potential of ranked-set sampling approaches for enhancing process monitoring mechanisms.

Ranked set sampling with varied order statistics for skew distributions

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 the methods not requiring actual measurements. The units corresponding to each rank are used in RSS and it performs better than simple random sampling (SRS) while estimating the population mean and other population parameters. In this paper, a new RSS procedure (RSSVO) for estimating the population mean of skew distributions is suggested. RSSVO measures only one or two order statistics depending upon the set size. The proposed estimator under RSSVO is then compared with the estimators based on SRS and RSS with equal allocation and Neyman’s optimal allocations. It is shown that the relative precisions of the estimators based on RSSVO are higher than those of the estimators based on SRS and RSS (both equal and Neyman’s optimal allocation) when the distributions under consideration are highly positive skew. Further, it is shown that, the performance of the proposed estimator increases as the skewness increases by using the example of lognormal distribution.

Inference for a Progressive-Stress Model Based on Ordered Ranked Set Sampling under Type-II Censoring

The progressive-stress accelerated life test is discussed under the ordered ranked set sampling procedure. It is assumed that the lifetime of an item under use stress is exponentially distributed and the law of inverse power is considered as the relationship between the scale parameter and the applied stress. The involved parameters are estimated using the Bayesian technique, under symmetric and asymmetric loss functions, based on ordered ranked set samples and simple random samples subject to type-II censoring. Real and simulated data sets are used to illustrate the theoretical results presented in this paper. Finally, a simulation study followed by numerical calculations is performed to evaluate the Bayesian estimation performance based on the two sampling types.

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.

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

<abstract> <p>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.</p> </abstract>

Information Generating Function of Ranked Set Samples.

In the present paper, we study the information generating (IG) function and relative information generating (RIG) function measures associated with maximum and minimum ranked set sampling (RSS) schemes with unequal sizes. We also examine the IG measures for simple random sampling (SRS) and provide some comparison results between SRS and RSS procedures in terms of dispersive stochastic ordering. Finally, we discuss the RIG divergence measure between SRS and RSS frameworks.

Cumulative residual extropy of minimum ranked set sampling with unequal samples

Recently, an alternative measure of uncertainty called cumulative residual extropy (CREX) was proposed by Jahanshahi et al. (2019). In this paper, we consider uncertainty measures of minimum ranked set sampling procedure with unequal samples (MinRSSU) in terms of CREX and its dynamic version and we compare the uncertainty and information content of CREX based on MinRSSU and simple random sampling (SRS) designs. Also, using simulation, we study new estimators of CREX for MinRSSU and SRS designs in terms of bias and mean square error. Finally, we provide a new discrimination measure of disparity between the distribution of MinRSSU and parental data SRS.

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.

Developing Mixed EWMA-CUSUM and CUSUM-EWMA control charts based on MRSS and DRSS procedures

The mixed EWMA-CUSUM and CUSUM-EWMA control charts are among the control charts provided in recent years by combining two exponentially weighted moving average and cumulative sum charts for efficient monitoring of the process mean. In this paper, we extended these mixed control charts by using new median ranked set sampling and double ranked set sampling procedures. The performance of the proposed mixed control charts is evaluated through extensive Monte Carlo simulations in terms of average run length criterion and the results show the proposed charts outperform the similar charts for detecting different shifts in process mean. Furthermore, a real data-set is also presented for explaining the implementation of the proposed control charts.

NGO online disclosures index in the presence of auxiliary information.

This study highlights the need for analysis of online disclosure practices followed by non-governmental organizations; furthermore, it justifies the crucial role of potential correlates of online disclosure practices followed by non-governmental organizations. We propose a novel index for analyzing the extent of online disclosure of non-governmental organizations (NGO). Using the information stored in an auxiliary variable, we propose a new estimator for gauging the average value of the proposed index. Our approach relies on the use of two factors: imperfect ranked-set sampling procedure to link the auxiliary variable with the study variable, and an NGO disclosure index under simple random sampling that uses information only about the study variable. Relative efficiency of the proposed index is compared with the conventional estimator for the population average under the imperfect ranked-set sampling scheme. Mathematical conditions required for retaining the efficiency of the proposed index, in comparison to the imperfect ranked set sampling estimator, are derived. Numerical scrutiny of the relative efficiency, in response to the input variables, indicates; if the variance of the NGO disclosure index is less than the variance of the estimator under imperfect ranked set sampling, then the proposed index is universally efficient compared to the estimator under imperfect ranked set sampling. If the condition on variances is unmet, even then the proposed estimator remains efficient if majority of the NGO share online data on the auxiliary variable. This work can facilitate nonprofit regulation in the countries where most of the non-governmental organizations maintain their websites.

Estimating Bark Eating Caterpillars Indarbela quadrinotata (walker) in Populus deltoides Using Ranked Set Sampling

<p>The problem of bark eating caterpillar, <em>Indarbela quadrinotata</em> infestation has been observed from variety of horticulture and forest tree species in India. The estimation of infestation of this caterpillar using conventional sampling methods was found difficult because counting the number of caterpillar in each tree is practically not feasible. Ranked set sampling (RSS) is a cost efficient method which provides improved estimators of mean and variance when actual measurement of the observations is difficult to obtain but a reasonable ranking of the units in the sample is relatively easy. In the present study, poplar, <em>Populus deltoides</em> plantation of Western Uttar Pradesh and Uttarakhand was taken for the assessment of <em>Indarbela quadrinotata</em> infestation. The RSS estimator of population mean and variance have been discussed and compared with the corresponding estimators from simple random sampling (SRS). The relative precision (RP) of RSS procedure with respect to the SRS for four different set sizes of <em>k </em>= 3, 5, 7, and 10 has been deliberated. It was seen that RP increase with the increment in <em>k</em>. The method of RSS was found suitable for the assessment of insect pest infestation.</p><p><strong>Keywords</strong><strong>: </strong><em>Indarbela quadrinotata</em>, <em>Populus deltoides</em>, simple random sampling, ranked set sample, order statistics.</p>

Cumulative Tsallis entropy for maximum ranked set sampling with unequal samples

In this paper, we consider the information content of maximum ranked set sampling procedure with unequal samples (MRSSU) in terms of Tsallis entropy which is a non-additive generalization of Shannon entropy. We obtain several results of Tsallis entropy including bounds, monotonic properties, stochastic orders, and sharp bounds under some assumptions. We also compare the uncertainty and information content of MRSSU with its counterpart in the simple random sampling (SRS) data. Finally, we develop some characterization results in terms of cumulative Tsallis entropy and residual Tsallis entropy of MRSSU and SRS data.

Extropy information of maximum and minimum ranked set sampling with unequal samples

Maximum ranked set sampling with unequal samples and minimum ranked set sampling with unequal samples procedures are two very useful modifications of ranked set sampling procedure. They allow for an increase in set size without introducing too many ranking errors. In this paper, we consider information content of minimum and maximum ranked set sampling with unequal samples in terms of extropy. We also compare the extropy of these two sampling data with that of simple random sampling and ranked set sampling data. Finally, we study the discrimination information among simple random sampling, ranked set sampling, minimum and maximum ranked set sampling with unequal samples data.

Parameter estimation for the exponential-Poisson distribution based on ranked set samples

In this paper, we discuss the point and interval estimation of the parameters of the exponential-Poisson distribution based on simple random samples, ranked set samples and maximum ranked set sampling procedure with unequal sample sizes. The maximum likelihood and Bayesian approaches are considered to derive the estimators. It seems that the Bayesian point estimates cannot be expressed in explicit forms, thus we propose the Metropolis-Hastings within Gibbs algorithm to approximate these estimates. A simulation study, as well as an example, are presented to evaluate and compare the proposed estimators. The paper ends with some remarks.

Estimating parameters of Morgenstern type bivariate distribution using bivariate ranked set sampling

This paper develops estimating parameters for Morgenstern type bivariatedistribution by using bivariate ranked set sampling procedure as an alterna-tive method to simple random sampling. This proposed procedure gives anopportunity to estimate all distribution's parameters simultaneously whichis not investigated in previous studies, yet. In the last part of this paper,simulation studies show properties of the new estimators and compare themwith some other existed estimators.

Mean estimate in ranked set sampling using a length-biased concomitant variable

In this paper, a ranked set sampling procedure with ranking based on a length-biased concomitant variable is proposed. The estimate for population mean based on this sample is given. It is proved that the estimate based on ranked set samples is asymptotically more efficient than the estimate based on simple random samples. Simulation studies are conducted to present the properties of the proposed estimate for finite sample size. Moreover, the consequence of ignoring length bias is also addressed by simulation studies and the real data analysis.

Measures of information for maximum ranked set sampling with unequal samples

ABSTRACTBiradar and Santosha (2014) proposed maximum ranked set sampling procedure with unequal samples (MRSSU) to estimate the mean of the exponential distribution. In this paper, we consider information measures of MRSSU in terms of Shannon entropy, Rényi entropy and Kullback-Leibler (KL) information. We also compare the uncertainty and information content of MRSSU with simple random sampling and ranked set sampling data. Finally, we develop some characterization results in terms of cumulative entropy and failure entropy of MRSSU.

Bayesian estimation for Rayleigh distribution based on ranked set sampling

The Rayleigh distribution is an important model in applications such as noise theory, height of the sea waves and wave length. In this paper, we provide Bayesian estimation for a parameter of the Rayleigh distribution based on simple random sample (SRS) and ranked set sampling (RSS) and maximum ranked set sampling procedure with unequal samples (MRSSU) in two cases, one cycle and m-cycle. We also obtain the Bayes estimators by using square-root inverted-gamma and Jeffreys prior under squared error loss function and general entropy loss function and LINEX function. Finally, we compute the bias and mean squared error of an estimator under squared error and compare its with the corresponding RSS and MRSSU through Monte Carlo simulations.