Ranked Set Sampling Research Articles

Empirical Bayes Likelihood for Exponential Distribution Family under Ranked Set Sampling and Dependent Data

Empirical Bayes Likelihood for Exponential Distribution Family under Ranked Set Sampling and Dependent Data

Residual extropy in ranked set sampling: Properties, comparative analysis, and estimation

Ranked set sampling (RSS) has gained significant significance in numerous practical domains, such as environmental and ecological studies, and statistical genetics. This article focuses on investigating the concept of extropy as a measure of residual uncertainty in RSS. It is devoted to discussing various monotone properties and characterization results associated with the residual extropy of RSS. Additionally, a comparative analysis is conducted between the residual extropy of RSS and its counterpart in simple random sampling. Optimal minima and maxima values for the residual extropy of RSS are determined. To further contribute to the field, a consistent estimator for the residual extropy of RSS is proposed. The effectiveness of this estimator is demonstrated through three illustrative examples, highlighting its performance in practical scenarios.

On the Estimation of Survival Rate Using Ranked Set Sampling Design

The Nigerian pensioners have high expectations from the government to ensure an effective implementation of pension regulations existing in the country. These expectations arise from the need to have sustainable standard of living in retirement and their benefits paid as at when due. However, the government does not know how many retirees will be alive at a particular period of time to draw fund from the pension account. This calls for regular verification of pensioners by Pension Transitional Arrangements Directorate (PTAD) at national level, office of the accountant general for State level and Local Government Pensions Board for Unified Local Government Council. This process exposed pensioners to stress related problems and some pensioners even die during such verification exercise. Again, it gives rise to varying set of problems that limit the capacity of the stakeholders within Nigeria pension industry to meet pensioner’s expectations. Survival rate of these retirees is key important statistic to the government for adequate preparation for their terminal benefits and to provide other social packages for this vulnerable group of people. However, this statistic is lacking in the State. Consequently, this work intends to address this problem by using the theory of Ranked Set Sampling (RSS) for Survival analysis to estimate the Survival rate of the retirees which will help the government in making adequate budgetary provisions to the Nigeria Pension Industry. Analysis and evaluation are presented.

Statistical inference and data analysis for inverted Kumaraswamy distribution based on maximum ranked set sampling with unequal samples

A very useful modification to ranked set sampling (RSS) that allows a larger set size without significantly increasing ranking errors is the maximum ranked set sampling with unequal samples (MRSSU) approach. This article covers the parameter estimation of the inverted Kumaraswamy distribution using MRSSU and RSS designs. The maximum likelihood and Bayesian estimation techniques are considered. The regarded Bayesian estimation technique is determined in the case of non-informative and informative priors represented by Jeffreys and gamma priors, respectively. Squared error and minimum expected are the two loss functions that are employed. We presented a simulation study to evaluate the performance of the recommended estimations using root mean squared error and relative bias. The Bayes point estimates were computed using the Metropolis–Hastings algorithm. Additional conclusions have been made based on actual geological data regarding the intervals between Kiama Blowhole’s 64 consecutive eruptions. Based on the same number of measured units, the results of simulation and real data analysis showed that MRSSU estimators performed much better than their RSS counterparts.

On the efficiency of paired ranked set sampling for estimating the population mean in the presence of non-response

Non-response is a common problem faced by surveyors while conducting surveys; this introduces a potential bias in the estimates of population parameters. One method of dealing with non-response is subsampling of the non-respondents, which increases precision in estimates by increasing the sample size. This study proposes an unbiased mean estimator in the presence of non-response using the Paired Ranked Set Sampling (PRSS) technique. The proposed estimator is based on a suggested strategy for adapting the subsampled units into the initial sample. Variance of the proposed estimator is derived, and conditions are provided for which the proposed estimator performs better than existing estimators. We conduct a simulation study to evaluate the precision of the proposed estimator in comparison with other existing estimators for estimating the population mean. In simulation, we assume populations based on normal distribution, exponential distribution, and real-life data on abalone. Simulation results show that the proposed mean estimator exhibits a higher probability of precisely estimating the finite population mean.

Efficient Control Chart for the Process Location Based on Dual-Rank Ranked Set Sampling

Efficient Control Chart for the Process Location Based on Dual-Rank Ranked Set Sampling

A novel ranked k-nearest neighbors algorithm for missing data imputation

Missing data is a common problem in many domains that rely on data analysis. The k Nearest Neighbors imputation method has been widely used to address this issue, but it has limitations in accurately imputing missing values, especially for datasets with small pairwise correlations and small values of k. In this study, we proposed a method, Ranked k Nearest Neighbors imputation that uses a similar approach to k Nearest Neighbor, but utilizing the concept of Ranked set sampling to select the most relevant neighbors for imputation. Our results show that the proposed method outperforms the standard k nearest neighbor method in terms of imputation accuracy both in case of Missing Completely at Random and Missing at Random mechanism, as demonstrated by consistently lower MSIE and MAIE values across all datasets. This suggests that the proposed method is a promising alternative for imputing missing values in datasets with small pairwise correlations and small values of k. Thus, the proposed Ranked k Nearest Neighbor method has important implications for data imputation in various domains and can contribute to the development of more efficient and accurate imputation methods without adding any computational complexity to an algorithm.

Ranked Set Sampling Based Regression Estimators in Two-Stage Sampling Design

Ranked Set Sampling Based Regression Estimators in Two-Stage Sampling Design

Optimizing population mean estimation under ranked set sampling with applications to Engineering

This article aims to develop two novel mean estimators of finite populations under ranked set sampling. The suggested estimators result in a high-efficiency gain due to their efficient formulation by taking the linear combination of classical estimators using optimization constants. We also discuss the theoretical properties and derive bias and mean squared error up to the first order of approximation. To theoretically validate our proposed estimators, we derive the conditions under which our estimators prevail over the competing estimators. The findings suggest that when ranked set sampling is implemented effectively, it saves cost and improves precision, serving as a potent instrument for improved decision-making, specifically in engineering applications, such as environmental monitoring, resource management, and quality control. An empirical and simulation study has been conducted using real and synthetic data to validate our methodology empirically. The suggested estimators offer a significant contribution to survey sampling in estimating mean under ranked set sampling. Further, the proposed estimator can be seamlessly adapted in other sampling designs such as simple random sampling, stratified random sampling, cluster sampling, etc, as well as in estimating other parameters such as variance, skewness, coefficient of correlation, etc. in various domains.

Analysis of dependent complementary competing risks data from a generalized inverted family of lifetime distributions under a maximum ranked set sampling procedure with unequal samples

This paper explores analysis of a dependent complementary competing risks model when the failure causes are distributed by the proposed generalized inverted family of lifetime distributions. Under maximum ranked set sampling with unequal samples (MRSSU), statistical inference of model parameters and reliability indices is discussed under classical frequentist and Bayesian approaches, respectively. Maximum likelihood estimators along with their existence and uniqueness are obtained for model parameters, and associated approximate confidence intervals are constructed in consequence. Bayesian estimation is also performed with respect to general flexible priors, and the Markov Chain Monte Carlo (MCMC) algorithm is proposed for complex posterior computation. The study further examines classical and Bayesian estimations with order restriction of parameters when additional historical information is available in the MRSSU scenario. Finally, the performance of different results is evaluated through numerical simulations and a real data example is presented for demonstrating the application of our methods.

Robust estimators for the log-logistic model based on ranked set sampling

Robust estimators for the log-logistic model based on ranked set sampling

Except-Extremes Ranked Set Sampling for Estimating the Population Variance with Two Applications of Real Data Sets

The ranked set sampling (RSS) procedure was initially established by McIntyre (1952) for estimating the mean of forage and pasture yield as more precise than simple random sampling (SRS). Recently, Aldrabseh and Ismail (2023) suggested the except extreme RSS (EERSS) approach as a modification to RSS for estimating the population mean. In this paper, a new estimator of the population variance is proposed using the EERSS method. The mean squared error and bias equations of the new estimator are derived. When the underlying distribution is non-symmetric, a simulation study is conducted to evaluate the suggested estimator relative to SRS and RSS, based on the same number of measured units, in terms of the relative precision and bias values for several sample sizes. For symmetric distributions, the exact values of the bias and relative precision of the EERSS variance estimator are evaluated. Two real datasets are utilized to illustrate the performance of the suggested variance estimator. It is found that the EERSS variance estimator is more efficient than the SRS estimator and more precise than RSS in most cases, especially for small set sizes.

Weighted exponential parameters estimation using maximum ranked set sampling with unequal samples

The two-parameter weighted exponential distribution exhibits various intriguing characteristics and is a powerful tool for analyzing skewed datasets. This study focuses on enhancing the efficiency of parameter estimation for the scale and shape parameters of the weighted exponential distribution. We investigate several estimators utilizing maximum ranked set sampling with unequal samples (MaxRSSU) for the aforementioned parameters. A comparison is made between the estimators obtained through MaxRSSU and those derived from simple random sampling (SRS). Our numerical findings demonstrate that the estimators obtained through MaxRSSU outperform their SRS counterparts significantly in terms of efficiency. Furthermore, we provide a practical illustration by applying our approach to a real dataset.

On indirect estimation of small area parameters under ranked set sampling

In investigations of domains under post-stratified random sampling, it is difficult to get an acceptable precision for domain-specific estimates due to low sample sizes. Small area estimate, a popular technique that has been widely used over the past few decades, involves indirect estimating using the auxiliary data from the entire population. In this article, we utilize a ranked set sampling (RSS) technique to achieve a greater level of precision in area-specific estimations under the assumption that ranking the smaller sets is simple, inexpensive, and flawless. RSS optimizes sample size for a fixed degree of precision or increases precision for a fixed sample size. We create direct estimators for population total under homogeneous, ratio, and regression models that are area specific. To evaluate the effectiveness and application of the suggested RSS technique, data from the Pakistan Demographic Health Survey (PDHS 2017–18) and Iris flower data are used. The effectiveness of the RSS mechanism is supported by both theoretical characteristics and Bootstrapped tests.

Improved Ratio-type Exponential Estimator for Estimating Population Mean in Ranked Set Sampling

In this paper we propose a ratio-type exponential estimator for estimating population mean of the study variable under Ranked set sampling when auxiliary information is known. The bias and Mean square error of the proposed estimator has been derived up to the first degree of approximation. A simulation study has been carried out to judge the performance of the newly proposed estimator along with existing estimators. It is obtained that the proposed estimator is more efficient as compared to the competing estimators.

Threshold sampling

We consider the problem of sampling elements with some desired property from a large set, without testing the property of interest, but with the (probabilistic) assurance to have at least one match among the random sample. Like in ranked set sampling (RSS), we consider an infinite population under study, whose properties of interest are too expensive and/or time-consuming to measure. Unlike RSS, we are void of a ranking mechanism, so our sampling is done entirely blind. We show how it is nonetheless doable to assure, with controllably large likelihood, to either have at least one of the interesting elements in a random sample, or, contrarily, sample with the likewise assurance of not having one of the interesting elements in the sample. Our technique utilizes density bounds for distributions and threshold functions from random graph theory.

Reliability test for degradation data based on ranked set sampling

AbstractIn this article, we consider test for the two null hypotheses for and , two widely useful tests in reliability, based on ranked set sampling (RSS). We derive the likelihood ratio test as well as the associated exact and asymptotic results. Considering a fixed significance level and power of the test, we show that the proposed test statistic outperforms the existing test. In small sample cases, the proposed test leads to a much narrower confidence interval for the reliability function . Then, the test statistics obtained from simple random sampling and RSS schemes are compared through which, the efficiency of using RSS is demonstrated. For illustration, we apply the proposed test to a degradation data from the reliability literature. Upon using RSS, the cost of measurement gets reduced and efficiency gets improved, suggesting the importance and use of RSS data in reliability experiments and their design.

Preliminary estimators of population mean using ranked set sampling in the presence of measurement error and non-response error with applications and simulation study

In order to estimate the population mean in the presence of both non-response and measurement errors that are uncorrelated, the paper presents some novel estimators employing ranked set sampling by utilizing auxiliary information. Up to the first order of approximation, the equations for the bias and mean squared error of the suggested estimators are produced, and it is found that the proposed estimators outperform the other existing estimators analysed in this study. Investigations using simulation studies and numerical examples show how well the suggested estimators perform in the presence of measurement and non-response errors. The relative efficiency of the suggested estimators compared to the existing estimators has been expressed as a percentage, and the impact of measurement errors has been expressed as a percentage computation of measurement errors.

Using the Nanogonal Membership Function and Fuzzy Parameters for The Exponential-Rayleigh Distribution of Coved-19

In this paper, we discuss estimating the fuzzy parameters of the Exponential-Rayleigh distribution using the Progressive Censored sample for the Rank Set method to become the proposed Rank Set Sampling estimation Method (RSSEM) in Censoring sample using the Newton-Raphson method to determine the parameter estimate values. Then utilizing Al Karkh General Hospital-Ministry of Health and Environment in Iraq for providing information about the actual data for COVID-19. To ascertain the Chi-square test was used. The distribution of the using sample is the Exponential-Rayleigh distribution. (ER). Then, we estimate the probability density function, hazard function, and survival function. To follow the estimation of the parameters and ER distribution's fuzzy parameters, we use the suggested approach. Moreover, to find the efficiency of the estimators, we use the mean square error of the survival function:

Point and interval estimation of $$R=P(X>Y)$$ for the proportional reversed hazard family based on ranked set sampling

Point and interval estimation of $$R=P(X>Y)$$ for the proportional reversed hazard family based on ranked set sampling