Ranked Set Research Articles

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

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.

Constructing a Hospital Department Development-Level Assessment Model: Machine Learning and Expert Consultation Approach in Complex Hospital Data Environments.

Every hospital manager aims to build harmonious, mutually beneficial, and steady-state departments. Therefore, it is important to explore a hospital department development assessment model based on objective hospital data. This study aims to use a novel machine learning algorithm to identify key evaluation indexes for hospital departments, offering insights for strategic planning and resource allocation in hospital management. Data related to the development of a hospital department over the past 3 years were extracted from various hospital information systems. The resulting data set was mined using neural machine algorithms to assess the possible role of hospital departments in the development of a hospital. A questionnaire was used to consult senior experts familiar with the hospital to assess the actual work in each hospital department and the impact of each department's development on overall hospital discipline. We used the results from this questionnaire to verify the accuracy of the departmental risk scores calculated by the machine learning algorithm. Deep machine learning was performed and modeled on the hospital system training data set. The model successfully leveraged the hospital's training data set to learn, predict, and evaluate the working and development of hospital departments. A comparison of the questionnaire results with the risk ranking set from the departments machine learning algorithm using the cosine similarity algorithm and Pearson correlation analysis showed a good match. This indicates that the department development assessment model and risk score based on the objective data of hospital systems are relatively accurate and objective. This study demonstrated that our machine learning algorithm provides an accurate and objective assessment model for hospital department development. The strong alignment of the model's risk assessments with expert opinions, validated through statistical analysis, highlights its reliability and potential to guide strategic hospital management decisions.

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:

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.

Properties of Group Fairness Measures for Rankings

In recent years, several measures have been developed for evaluating group fairness of rankings. Given that these measures were developed with different application contexts and ranking algorithms in mind, it is not straightforward which measure to choose for a given scenario. Previous work has already laid out some categorizations of measures and explored relationships between these, however, there has not yet been a thorough mathematical analysis of practically grounded properties of individual measures. In this paper, we therefore apply an axiomatic approach to perform a comprehensive analysis of existing group fairness measures that have been developed in the context of fair ranking. To this end, we propose a set of fourteen properties for group fairness measures that consider different ranking settings. These properties specifically provide information about how fairness scores of ranked outputs can be interpreted and contextualized. For a given use case, one can then identify which properties are of interest, and select a measure based on whether it satisfies these properties. We further apply our properties on twelve existing group fairness measures, and through both empirical and theoretical results demonstrate that most of these measures only satisfy a small subset of the proposed properties. These findings highlight limitations of existing measures, and provide insights into how to evaluate and interpret different fairness measures in practical deployment. Overall, our work can assist practitioners in selecting appropriate group fairness measures for a specific application, and also aid researchers in designing and evaluating such measures.

General weighted extropy of minimum and maximum ranked set sampling with unequal samples

. In industrial, environmental, and ecological investigations, ranked set sampling is a sample method that enables the experimenter to use the whole range of population values. The ranked set sampling process can be modified in two extremely helpful ways: maximum ranked set sampling with unequal samples and minimum ranked set sampling with unequal samples. They permit an increase in set size without too many ranking errors being introduced. In this article, we are defining general weighted extropy (GWJ) of minimum and maximum ranked set samples when samples are of unequal size (minRSSU and maxRSSU, respectively). Stochastic comparison and monotone properties have been studied under different situations. Additionally, we compare the extropy of these two sampling data with that of ranked set sampling data and simple random sampling data. Bounds of GWJ of minRSSU and maxRSSU have been obtained. Finally, we investigate the weighted discrimination information between simple random sampling, ranked set sampling, and minimum and maximum ranked set sampling with unequal sample sizes. Some results for equality of GWJ of minRSSU and maxRSSU under symmetric assumption are also obtained.

New Modification of Ranked Set Sampling for Estimating Population Mean: Neutrosophic Median Ranked Set Sampling with an Application to Demographic Data

The study addressed the limitations of classical statistical methods when dealing with ambiguous data, emphasizing the importance of adopting neutrosophic statistics as a more effective alternative. Classical methods falter in managing uncertainty inherent in such data, necessitating a shift towards methodologies like neutrosophic statistics. To address this gap, the research introduced a novel sampling approach called “neutrosophic median ranked set sampling” and incorporated neutrosophic estimators tailored for estimating the population mean in the presence of ambiguity. This modification aims to address the inherent challenges associated with estimating the population mean when dealing with neutrosophic data. The methods employed involved modifying traditional ranked set sampling techniques to accommodate neutrosophic data characteristics. Additionally, neutrosophic estimators were developed to leverage auxiliary information within the framework of median-ranked set sampling, enhancing the accuracy of population mean estimation under uncertain conditions. The methods employed involved modifying traditional ranked set sampling techniques to accommodate neutrosophic data characteristics. Bias and mean squared error equations for the suggested estimators were provided, offering insights into their theoretical underpinnings. To illustrate the effectiveness and practical applications of the proposed methodology and estimators, a numerical demonstration and simulation study have been conducted using the R programming language. The key results highlighted the superior performance of the proposed estimators compared to existing alternatives, as demonstrated through comprehensive evaluations based on mean squared error and percentage relative efficiency criteria. The conclusions drawn underscored the effectiveness of the neutrosophic median ranked set sampling approach and suggested estimators in estimating the population mean under conditions of uncertainty, particularly when utilizing neutrosophic auxiliary information and validated real-life applicability. The methodology and estimators presented in the study were shown to yield interval-based results, providing a more realistic representation of uncertainty associated with population parameters. This interval estimation, coupled with minimum mean squared error considerations, enhanced the efficacy of the estimators in determining population mean values. The novelty of the work lies in its introduction of a tailored sampling approach and estimators designed specifically for neutrosophic data, filling a significant gap in the literature. By extending classical statistics to accommodate ambiguity, the study offers a substantial advancement in statistical methodology, particularly in domains where precise data is scarce and uncertainty is prevalent. Furthermore, the empirical validation through numerical demonstrations and simulation studies using the R programming language adds robustness to the proposed methodology and contributes to its practical applicability.

Simulation-Based Study on Extreme Ranked Set Sampling from Rician Distribution

The RSS approach is a useful method of sampling that reduces the cost and improves the representativeness of the population. It provides more efficient estimators than the competitors based on SRS. However, using RSS could be a difficult task to observe all the ranks. Thus, using only the extreme ranks eases the task and reduces the error in ranking. Samawi et al. (1996) proposed the method of Extreme Ranked Set Sampling (ERSS) to reduce errors in ranking and showed that the method gives an unbiased estimate of the population mean in the case of symmetric populations and it provides a more efficient estimator than SRS. However, the estimator of this method is biased when the distribution is skewed. Many researchers have considered ERSS, investigated several estimators, and studied their properties. In this paper, we adopt the ERSS technique when the samples are drawn from the Rician distribution. Several estimators have been studied, including arithmetic mean, geometric mean, harmonic mean, quadratic mean, median, variance, mean deviation, skewness, and kurtosis. Computer simulations were used to check the properties of these estimators and compared with the corresponding estimators using SRS. Some estimators based on ERSS are more efficient than the corresponding estimators from SRS, but some others are not.

PSI-SAW and PSI-MARCOS Hybrid MCDM Methods

This paper presents a study on the hybridization of Multi-Criteria Decision-Making (MCDM) methods: Preference Selection Index (PSI), Simple Additive Weighting (SAW), and Measurement Alternatives and Ranking according to COmpromise Solution (MARCOS). The hybridization was conducted between the PSI and the other two methods, resulting in new methods, namely PSI-SAW and PSI-MARCOS. For each specific problem, applying these two hybrid methods to rank alternatives among the available options produces three different sets of rankings: one created by PSI, one by the hybrid PSI-SAW, and one by the hybrid PSI-MARCOS. The accuracy of the proposed models was tested in three different cases. The test results show that both proposed models exhibit high accuracy. This study provides users with highly accurate and useful methods for MCDM.

Restrictions on Anosov subgroups of 𝑆𝑝(2𝑛,ℝ)

Let n ∈ N n\in \mathbb {N} and let Θ ⊂ { 1 , … , n } \Theta \subset \{1,\dots ,n\} be a nonempty subset. We prove that if Θ \Theta contains an odd integer, then any P Θ P_\Theta -Anosov subgroup of Sp ⁡ ( 2 n , R ) \operatorname {Sp}(2n,\mathbb {R}) is virtually isomorphic to a free group or a surface group. In particular, any Borel Anosov subgroup of Sp ⁡ ( 2 n , R ) \operatorname {Sp}(2n,\mathbb {R}) is virtually isomorphic to a free or surface group. On the other hand, if Θ \Theta does not contain any odd integers, then there exists a P Θ P_\Theta -Anosov subgroup of Sp ⁡ ( 2 n , R ) \operatorname {Sp}(2n,\mathbb {R}) which is not virtually isomorphic to a free or surface group. We also exhibit new examples of maximally antipodal subsets of certain flag manifolds; these arise as limit sets of rank 1 1 subgroups.

A Class of Ratio and Product Types Estimators of Mean of a Sensitive Variable Using Ranked Set Sampling

A Class of Ratio and Product Types Estimators of Mean of a Sensitive Variable Using Ranked Set Sampling

Modified median quartile double ranked set sampling for estimation of population mean

Environmental monitoring and assessment aim to gather data economically, without bias, using efficient and cost-effective sampling methods. One such traditional method is Ranked Set Sampling (RSS), often employed to achieve observational economy. This article introduces an innovative two-stage sampling approach for ranked set sampling (RSS) to get a more precise estimate of the population mean. Modified Median Quartile Double Ranked Set Sampling (MMQDRSS) highlights the ranked base technique's potential as a cost-effective sampling method. To evaluate the performance of the proposed estimator by using real-life data and conducting a simulation study to compare the relative efficiency of the proposed estimator with some existing methods.

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.

Bayesian mixture modelling with ranked set samples.

We consider the Bayesian estimation of the parameters of a finite mixture model from independent order statistics arising from imperfect ranked set sampling designs. As a cost-effective method, ranked set sampling enables us to incorporate easily attainable characteristics, as ranking information, into data collection and Bayesian estimation. To handle the special structure of the ranked set samples, we develop a Bayesian estimation approach exploiting the Expectation-Maximization (EM) algorithm in estimating the ranking parameters and Metropolis within Gibbs Sampling to estimate the parameters of the underlying mixture model. Our findings show that the proposed RSS-based Bayesian estimation method outperforms the commonly used Bayesian counterpart using simple random sampling. The developed method is finally applied to estimate the bone disorder status of women aged 50 and older.

Inference of Constant-Stress Model of Fréchet Distribution under a Maximum Ranked Set Sampling with Unequal Samples

Inference of Constant-Stress Model of Fréchet Distribution under a Maximum Ranked Set Sampling with Unequal Samples

Testing the Significance of Ranked Gene Sets in Genome-wide Transcriptome Profiling Data Using Weighted Rank Correlation Statistics.

Popular gene set enrichment analysis approaches assumed that genes in the gene set contributed to the statistics equally. However, the genes in the transcription factors (TFs) derived gene sets, or gene sets constructed by TF targets identified by the ChIP-Seq experiment, have a rank attribute, as each of these genes have been assigned with a p-value which indicates the true or false possibilities of the ownerships of the genes belong to the gene sets. Ignoring the rank information during the enrichment analysis will lead to improper statistical inference. We address this issue by developing of new method to test the significance of ranked gene sets in genome-wide transcriptome profiling data. A method was proposed by first creating ranked gene sets and gene lists and then applying weighted Kendall's tau rank correlation statistics to the test. After introducing top-down weights to the genes in the gene set, a new software called "Flaver" was developed. Theoretical properties of the proposed method were established, and its differences over the GSEA approach were demonstrated when analyzing the transcriptome profiling data across 55 human tissues and 176 human cell-lines. The results indicated that the TFs identified by our method have higher tendency to be differentially expressed across the tissues analyzed than its competitors. It significantly outperforms the well-known gene set enrichment analyzing tools, GOStats (9%) and GSEA (17%), in analyzing well-documented human RNA transcriptome datasets. The method is outstanding in detecting gene sets of which the gene ranks were correlated with the expression levels of the genes in the transcriptome data.

Reliability Estimation in Stress Strength for Generalized Rayleigh Distribution Using a Lower Record Ranked Set Sampling Scheme

This paper explores the likelihood and Bayesian estimation of the stress–strength reliability parameter (R) based on a lower record ranked set sampling scheme from the generalized Rayleigh distribution. Maximum likelihood and Bayesian estimators as well as confidence intervals of R are derived and their properties are studied. Furthermore, two parametric bootstrap confidence intervals are introduced in the paper. A comparative simulation study is conducted to assess the effectiveness of these four confidence interval methodologies in estimating R. The application of the methods is demonstrated using real data on fiber strength to showcase their practicability and relevance in the industry.