Ranked Set Research Articles

On Estimating Multi- Stress Strength Reliability for Inverted Kumaraswamy Under Ranked Set Sampling with Application in Engineering

The terrible operating constraints of many real-world events cause systems to malfunction regularly. The failure of systems to perform their intended duties when they reach their lowest, highest, or both extreme operating conditions is a phenomenon that researchers rarely focus on. The multi-stress strength reliability R=P(W<X<Z)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$R = P(W<X<Z)$$\\end{document} is deemed in this study for a component whose strength X falls between two stresses, W, and Z, where X, W, and Z are independently inverted Kumaraswamy distributed. Both maximum likelihood and maximum product spacing procedures are employed to obtain the reliability estimator under simple random sampling (SRS) and ranked set sampling (RSS) methodologies. Four scenarios for reliability estimators are considered. The reliability estimator in the first and second cases can be determined by applying the same sample design (RSS/SRS) to the strength and stress distributions. When the sample data for W and Z originate from RSS while those for X are acquired from SRS, the third reliability estimator is calculated. The drawn data of the strength and stress random variables, which are obtained from SRS and RSS, respectively, are taken into consideration in the final scenario. The effectiveness of the suggested estimators is compared using a comprehensive computer simulation. Lastly, three real data sets have been used to determine reliability estimators.

Escaping Fatou components with disjoint hyperbolic limit sets

We construct automorphisms of C2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\mathbb {C}}}^2$$\\end{document} of constant Jacobian with a cycle of escaping Fatou components, on which there are exactly two limit functions, both of rank 1. On each such Fatou component, the limit sets for these limit functions are two disjoint hyperbolic subsets of the line at infinity. In the literature there are currently very few examples of automorphisms of C2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\mathbb {C}}}^2$$\\end{document} with rank one limit sets on the boundary of Fatou components. To our knowledge, this is the first example in which such limit sets are hyperbolic, and moreover different limit sets of rank 1 coexist.

An nLCA approach to support consumer meal decisions: a New Zealand case study of toppings on toast

IntroductionThis study investigates the development and potential application of a nutritional Life Cycle Assessment (nLCA) method to rank meals, using a case study of a “toppings on toast” (ToTs) meal. Methodological issues are investigated in the context of application to support consumers to make more informed food choices at the meal level.MethodsFourteen selected “toppings on toast” (ToTs) commonly consumed in New Zealand (NZ) were evaluated for their climate change impacts and nutritional value using the serve size of each topping as the functional unit (FU). NZ-specific climate change values were obtained from an existing database and recent literature. Nutritional value was calculated using the NRF family of indices – specifically the NRF9.3 and NRF28.3 indices (the latter constructed for this study to include all nutrients in the selected toppings for which reference values were available) and presented in a separate midpoint nutrition impact category. The NRF and climate change scores were assigned quartile-based weights, and the weight of each index score was averaged with that of the climate change score. Based on these average values, the toppings were ranked in two ranking sets (one for each index). In a sensitivity analysis, two alternative reference units were also used (100 g and 100 kcal) to investigate how different FUs influenced the final rankings.ResultsThe results showed that use of one or other NRF index affected the magnitude of the nLCA results; however, the rankings of the ToTs based on the nLCA results did not change much between the two indices. Avocado and peanut butter performed the best (top two ranks), and bacon, butter, and cheese were the poorest performers (bottom two ranks), for both the ranking sets. The toppings which did change ranks mostly moved up or down by only one position. Thus, the results of this case study suggest that the NRF9.3 index is sufficient to determine overall the best, medium, and worst performing toppings in the ToT meal context. However, the results also showed that water-soluble vitamins and unsaturated fats included in the NRF28.3 index contributed significantly to the nutritional scores for most of the toppings and were instrumental in the rank changes for the toppings which are particularly rich in these nutrients.DiscussionThus, for a more diverse range of toppings/meals, an expanded index including these nutrients can generate more nuanced rankings. This study contributes to the nascent but fast-growing nLCA research field, particularly within the meal context. The method used in this case study could be applied in food composition databases, restaurant menus, and websites/apps that provides recipes for meals. However, the study also highlighted the potentially significant variability in climate change and nutritional values in the toppings associated with different production practices, seasonality, and different varieties of the same product. Any future development of nLCA-based meal level rankings should address this variability and communicate it to the consumer.

Exploiting Instance-level Relationships in Weakly Supervised Text-to-Video Retrieval

Text-to-Video Retrieval is a typical cross-modal retrieval task that has been studied extensively under a conventional supervised setting. Recently, some works have sought to extend the problem to a weakly supervised formulation, which can be more consistent with real-life scenarios and more efficient in annotation cost. In this context, a new task called Partially Relevant Video Retrieval (PRVR) is proposed, which aims to retrieve videos that are partially relevant to a given textual query, i.e., the videos containing at least one semantically relevant moment. Formulating the task as a Multiple Instance Learning (MIL) ranking problem, prior arts rely on heuristics algorithms such as a simple greedy search strategy and deal with each query independently. Although these early explorations have achieved decent performance, they may not fully utilize the bag-level label and only consider the local optimum, which could result in suboptimal solutions and inferior final retrieval performance. To address this problem, in this paper, we propose to exploit the relationships between instances to boost retrieval performance. Based on this idea, we creatively put forward: 1) a new matching scheme for pairing queries and their related moments in the video; 2) a new loss function to facilitate cross-modal alignment between two views of an instance. Extensive validations on three publicly available datasets have demonstrated the effectiveness of our solution and verified our hypothesis that modeling instance-level relationships is beneficial in the MIL ranking setting. Our code will be publicly available at https://github.com/xjtupanda/BGM-Net.

Estimation of population mean using ranked set sampling in the presence of measurement errors

Ranked set sampling is widely acknowledged for its superior efficiency compared with simple random sampling. Only a small amount of work has been conducted using ranked set sampling when measurement errors are present. This study introduces innovative estimators utilizing ranked set sampling to assess the population mean when faced with both correlated and uncorrelated measurement errors. The expressions for the bias and mean squared error of the proposed estimators are derived up to the first-order approximation, revealing their superior performance compared to the other examined estimators. The efficacy of the suggested estimators in handling measurement errors was demonstrated through numerical illustration and simulation study investigations. The recommended estimators are further compared to the existing ones using the percentage relative efficiency and mean squared error, and the impact of measurement errors on the results is highlighted through the percentage computation of measurement errors. The innovative estimators suggested were formulated by judiciously incorporating ratio, exponential, and log estimators. Numerical examples involving expenditure and income, as well as simulated data generated from a normal population using R software, affirm the superior performance of the proposed estimators over existing ones such as the usual mean estimator and those proposed by Vishwakarma and Singh (2022), as evidenced by the higher percent relative efficiency and lower mean squared error. The evaluation of the percentage contribution of measurement error values confirms the impact of measurement errors on the properties of the estimators.

A statistical framework for a new Kavya-Manoharan Bilal distribution using ranked set sampling and simple random sampling

In survival and stochastic lifespan modeling, numerous families of distributions are sometimes considered unnatural, unjustifiable theoretically, and occasionally superfluous. Here, a novel parsimonious survival model is developed using the Bilal distribution (BD) and the Kavya-Manoharan (KM) parsimonious transformation family. In addition to other analytical properties, the forms of probability density function (PDF) and behavior of the distributions' hazard rates are analyzed. The insights are theoretical as well as practical. Theoretically, we offer explicit equations for the single and product moments of order statistics from Kavya-Manoharan Bilal Distribution. Practically, maximum likelihood (ML) technique, which is based on simple random sampling (SRS) and ranked set sampling (RSS) sample schemes, is employed to estimate the parameters. Numerical simulations are used as the primary methodology to compare the various sampling techniques.

Estimation of Gumbel Distribution Based on Ordered Maximum Ranked Set Sampling with Unequal Samples

Sample selection is one of the most important factors in estimating the unknown parameters of distributions, as it saves time, saves effort, and gives the best results. One of the challenges is deciding on a suitable distribution estimate technique and adequate sample selection to provide the best results in comparison with earlier research. The method of moments (MOM) was decided on to estimate the unknown parameters of the Gumbel distribution, but with four changes in the sample selection, which were simple random sample (SRS), ranked set sampling (RSS), maximum ranked set sampling (MRSS), and ordered maximum ranked set sampling (OMRSS) techniques, due to small sample sizes. The MOM is a traditional method for estimation, but it is difficult to use when dealing with RSS modification. RSS modification techniques were used to improve the efficiency of the estimators based on a small sample size compared with the usual SRS estimator. A Monte Carlo simulation study was carried out to compare the estimates based on different sampling. Finally, two datasets were used to demonstrate the adaptability of the Gumbel distribution based on the different sampling techniques.

Bivariate scoring rules: Unifying the characterizations of positional scoring rules and Kemeny's rule

This paper studies social preference functions (SPFs), which map the voters' ordinal preferences over a set of alternatives to a non-empty set of strict rankings over the alternatives. Maybe the most prominent SPFs are positional scoring rules and Kemeny's rule. While these two types of rules behave intuitively quite differently, they are axiomatically surprisingly similar and we thus provide a joint axiomatic characterization of these SPFs. To this end, we introduce the class of bivariate scoring rules which generalize Kemeny's rule by weighting comparisons between alternatives depending on their positions in the voters' preference relations. In particular, this class contains both Kemeny's rule and all positional scoring rules. As our main result, we then characterize the set of bivariate scoring rules as the only SPFs that satisfy—aside from some standard axioms—mild consistency conditions for variable electorates and variable agendas. As corollaries of this result, we also derive variants of the well-known characterizations of positional scoring rules by Smith (1973) and of Kemeny's rule by Young (1988). Thus, our result unifies the independent streams of research on positional scoring rules and Kemeny's rule by giving a joint axiomatic basis of these SPFs.

On some efficient logarithmic type estimators under stratified ranked set sampling

On some efficient logarithmic type estimators under stratified ranked set sampling

Exploring the dependability of Combined Ratio Estimators in Stratified Ranked Set Sampling: Insights from COVID-19 data

In this study, we introduce a novel combined ratio type estimator within the framework of Stratified Ranked Set Sampling to estimate the population mean of the study variable by incorporating bivariate auxiliary information. We conduct a comprehensive comparative analysis, including traditional combined ratio, combined regression, Shabbir and Khan [13], and Bhushan and Kumar [37] estimators. We assess the bias and mean squared error of the proposed estimator under the initial degree of approximation. The data source consists of COVID-19 data up to July 2023. Through empirical investigation and simulation studies, our proposed estimator consistently demonstrates superior performance compared to its counterparts, exhibiting the highest relative efficiency. These findings underscore the practical significance of our research in public health and decision-making, emphasizing the potential of this estimator to provide more accurate and reliable estimates in various applications involving ranked set sampling and auxiliary information.

A Refinement of Ratio Estimation in Ranked Set Sampling and Stratified Ranked Set Sampling Approaches

Estimation of population mean is a persistent subject issue in sampling surveys and many discrete efforts have been paid by various researchers to enhance the precision of the estimates by utilizing the correlated auxiliary information. In connection with this an improved version of ratio estimator are presented in this paper under the ranked set sampling scheme and stratified ranked set sampling scheme. Comparison amongst estimators is made in terms of Mean Square Errors ( ) and Percentage Relative Efficiencies ( ). The expression for of the proposed estimator is pinned-down to first order of approximations. It turns out from both simulation studies as well as real data set that the proposed estimator dominates its existing counterpart estimators.

Statistical inference for a novel distribution using ranked set sampling with applications

Working on symmetrical or asymmetrical data is complicated since each requires a different probability density function. Many statistical distributions can be used for these data types, where choosing one should be satisfied with the correct data type. So, we apply the ranked set sampling technique, which is essential in gaining data when dealing with units in a population is expensive. However, their classification is simple according to the variable of interest. The Unit Generalized Rayleigh distribution has recently played a crucial role in analyzing symmetrical or asymmetrical complex data sets specifically in modeling claim and risk data used in actuarial and financial studies, and its density can take different symmetric and asymmetric possible shapes. It is proposed in various areas, such as reliability, survival, economics, actuarial science, and insurance. We applied the ranked set sampling design in this article for gaining the model parameter estimations of the unit generalized Rayleigh model. Different estimation procedures and risk measures are computed. Moreover, the performance of these measures is illustrated via numerical simulation experiments. Under different proposed estimators, we conduct the validation of the suggested ranked set sampling design via numerous Monte Carlo simulation experiments by computing average bias and mean squared errors. At the end, we illustrated two real applications of the financial area for demonstrating the potential and the supremacy of the proposed ranked set sampling estimators.

Saturating linear sets of minimal rank

Saturating sets are combinatorial objects in projective spaces over finite fields that have been intensively investigated in the last three decades. They are related to the so-called covering problem of codes in the Hamming metric. In this paper, we consider the recently introduced linear version of such sets, which is, in turn, related to the covering problem in the rank metric. The main questions in this context are how small the rank of a saturating linear set can be and how to construct saturating linear sets of small rank. Recently, Bonini, Borello, and Byrne provided a lower bound on the rank of saturating linear sets in a given projective space, which is shown to be tight in some cases. In this paper, we provide construction of saturating linear sets meeting the lower bound and we develop a link between the saturating property and the scatteredness of linear sets. The last part of the paper is devoted to show some parameters for which the bound is not tight.

Generalized multivariate EWMA control chart supplemented with bivariate ranked set techniques

ABSTRACT Existing univariate exponential weighted moving average (EWMA) control charts with ranked set schemes are used for monitoring related characteristics independently. Also, existing multivariate EWMA control charts are generally applicable for simple random sampling (SRS) based processes. In this work, a generalized multivariate EWMA control chart is proposed with bivariate ranked set techniques (BVRST) for simultaneously monitoring. Furthermore, an extensive comparative analysis between proposed generalized multivariate EWMA and classical control chart is conducted. In this regard, we have used various performance measures, which cover average run length, median of run length, relative average run length, performance comparison index, and extra quadratic loss. The performance measures are obtained using the Monte Carlo simulation (MCS) approach. Results revealed that the proposed generalized multivariate EWMA control chart has an outstanding detection ability relative to the existing multivariate control charts. Additionally, existing multivariate control charts are found special cases of the proposed control chart. A real-life example from the agriculture field is included in which chemical properties (residual sodium and calcium-magnesium contents) of irrigation water are monitored through the control charts. The results revealed that the proposed control chart is proficient in diagnosing small variations in the chemical characteristics relative to the existing control charts.

Inferring from an imprecise Plackett–Luce model: Application to label ranking

The Plackett–Luce model is a popular parametric probabilistic model to define distributions between rankings of objects, modelling for instance observed preferences of users or ranked performances of algorithms. Since such observations may be scarce (users may provide partial preferences, or not all algorithms are run for a given experiment), it may be useful to consider the case where the parameters of the Plackett–Luce model are imprecisely known. In this paper, we first introduce the imprecise Plackett–Luce model, induced by a set of parameters (for instance, parameters with a high relative likelihood). Given a set of possible parameters for the model, we then provide an efficient algorithm to make cautious inferences, returning sets of possible optimal rankings (for instance in the form of partial orders). We illustrate the use of our imprecise model on label ranking, a specific kind of supervised learning.

Emoji’s sentiment score estimation using convolutional neural network with multi-scale emoji images

Emojis are any small images, symbols, or icons that are used in social media. Several well-known emojis have been ranked and sentiment scores have been assigned to them. These ranked emojis can be used for sentiment analysis; however, many new released emojis have not been ranked and have no sentiment score yet. This paper proposes a new method to estimate the sentiment score of any unranked emotion emoji from its image by classifying it into the class of the most similar ranked emoji and then estimating the sentiment score using the score of the most similar emoji. The accuracy of sentiment score estimation is improved by using multi-scale images. The ranked emoji image data set consisted of 613 classes with 161 emoji images from three different platforms in each class. The images were cropped to produce multi-scale images. The classification and estimation were performed by using convolutional neural network (CNN) with multi-scale emoji images and the proposed voting algorithm called the majority voting with probability (MVP). The proposed method was evaluated on two datasets: ranked emoji images and unranked emoji images. The accuracies of sentiment score estimation for the ranked and unranked emoji test images are 98% and 51%, respectively.

Bayesian Regression Analysis using Median Rank Set Sampling

Bayesian estimation of the linear regression parameter system is considered by deploying Median Rank Set Sampling (MRSS). The full conditional distributions and the associated posterior distribution are obtained. Therefore, based on Markov Chain Monte Carlo simulation, the Bayesian point estimates and credible intervals for the regression parameters are determined. To measure the efficiency of the obtained Bayesian estimates concerning the frequentist estimates we compute the asymptotic relative efficiency of the obtained Bayesian estimates using Markov Chain Monte Carlo simulation.

An Efficient CDF Estimator Based on Dual-Rank Ranked Set Sampling with an Application to Body Mass Index Data

An Efficient CDF Estimator Based on Dual-Rank Ranked Set Sampling with an Application to Body Mass Index Data

Adaptive Multi-Criteria-Based Load Balancing Technique for Resource Allocation in Fog-Cloud Environments

Recently, to deliver services directly to the network edge, fog computing, an emerging and developing technology, acts as a layer between the cloud and the IoT worlds. The cloud or fog computing nodes could be selected by IoTs applications to meet their resource needs. Due to the scarce resources of fog devices that are available, as well as the need to meet user demands for low latency and quick reaction times, resource allocation in the fog-cloud environment becomes a difficult problem. In this problem, the load balancing between several fog devices is the most important element in achieving resource efficiency and preventing overload on fog devices. In this paper, a new adaptive resource allocation technique for load balancing in a fog-cloud environment is proposed. The proposed technique ranks each fog device using hybrid multi-criteria decision- making approaches Fuzzy Analytic Hierarchy Process (FAHP) and Fuzzy Technique for Order Performance by Similarity to Ideal Solution (FTOPSIS), then selects the most effective fog device based on the resulting ranking set. The simulation results show that the proposed technique outperforms existing techniques in terms of load balancing, response time, resource utilization, and energy consumption. The proposed technique decreases the number of fog nodes by 11%, load balancing variance by 69% and increases resource utilization to 90% which is comparatively higher than the comparable methods.

An Efficient Variant of Ranked Set Sampling, Probability Proportional to Size with Application to Economic Data

In this paper, we apply the Ranked Set Sampling (RSS) technique to economic data in the form of homescan market research data set for the meat food group. The RSS method is then extended to select sampling units based on the Probability-Proportional-to-Size (PPS) approach. The new proposed ranked set sampling, using the PPS-derived method, RPPS, is assessed via Monte Carlo investigations and an extensive homescan data set to evaluate its performances. The results are promising and in line with theoretical and simulation studies, showing that the RPPS technique is more reliable and has a smaller variance than the PPS route.