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The quality performance of many vital systems depends on how long the units are performing; hence, research works started focusing on increasing the reliability of systems while taking into consideration that many factors may cause the failures of operating systems. In this study, the combination of a parametric generalized linear failure rate distribution model and an adaptive progressive Type-II censoring scheme for practical purposes is explored. A comprehensive investigation is performed on the risk factors that cause failure and determines which of the factors has a more harmful effect on the units. A lifetime experiment is performed under the condition of an adaptive progressive Type-II censoring scheme to obtain observations as a result of the competing factors of failures. The obtained observations are assumed to follow a three-parameter generalized linear failure rate distribution and are assumed to be competing to cause failure. Two statistical inference methods are employed for estimating this model's parameters: the frequentist maximum likelihood method and the Bayesian approach. Our model's validity is demonstrated through extensive simulations and real data applications in the medical and electrical engineering fields. [ABSTRACT FROM AUTHOR]

Simple Summary: Despite guidelines recommending surgery as part of treatment for stage I small cell lung cancer (SCLC), its application remains inconsistent, and its role in stages II and III is under debate. In absence of current randomized control trials this meta-analysis compared surgery to non-surgical treatment for stages I to III SCLC. After a systematic review, ten studies with a total of 95,323 patients were analyzed. The analysis found no significant differences in patient characteristics between the surgery and non-surgery groups. The 5-year survival rate for resected patients was significantly higher compared to non-surgically treated patients. This finding was valid also for patients in stages II and III. Surgery might significantly improve survival in SCLC patients and should be considered in treatment planning even in higher stages. Introduction: Despite clear guideline recommendations, surgery is not consistently carried out as part of multimodal therapy in stage I small cell lung cancer (SCLC) patients. The role of surgery in stages II and III is even more controversial. In the absence of current randomized control trials (RCT), we performed a meta-analysis comparing surgery versus non-surgical treatment in stage I to III SCLC patients. Methods: A systematic review of the literature was conducted on 1 July 2023, focusing on studies pertaining to the impact of surgery on small cell lung cancer (SCLC). These studies were evaluated using the ROBINS-I tool. Statistical analyses, including I² tests, Q-statistics, DerSimonian-Laird tests, and Egger regression, were performed to assess the data. In addition, 5-year survival rates were analyzed. The meta-analysis was conducted according to PRISMA standards. Results: Among the 6826 records identified, 10 original studies encompassing a collective cohort of 95,323 patients were incorporated into this meta-analysis. Heterogeneity was observed across the included studies, with no discernible indication of publication bias. Analysis of patient characteristics revealed no significant differences between the two groups (p-value > 0.05). The 5-year survival rates in a combined analysis of patients in stages I–III were 39.6 ± 15.3% for the 'surgery group' and 16.7 ± 12.7% for the 'non-surgery group' (p-value < 0.0001). SCLC patients in stages II and III treated outside the guideline with surgery had a significantly better 5-year survival compared to non-surgery controls (36.3 ± 20.2% vs. 20.2 ± 17.0%; p-value = 0.043). Conclusions: In the absence of current RCTs, this meta-analysis provides robust suggestions that surgery might significantly improve survival in all SCLC stages. Non-surgical therapy could lead to a shortening of life. The feasibility of surgery in non-metastatic SCLC should always be evaluated as part of a multimodal treatment. [ABSTRACT FROM AUTHOR]

Finite Gaussian mixture models are powerful tools for modeling distributions of random phenomena and are widely used for clustering tasks. However, their interpretability and efficiency are often degraded by the impact of redundancy and noise, especially on high-dimensional datasets. In this work, we propose a generative graphical model for parsimonious modeling of the Gaussian mixtures and robust unsupervised learning. The model assumes that the data are generated independently and identically from a finite mixture of robust factor analyzers, where the features' salience is adjusted by an active set of latent factors to allow a violation of the local independence assumption. For the model inference, we propose a structured variational Bayes inference framework to realize simultaneous clustering, model selection and outlier processing. Performance of the proposed algorithm is evaluated by conducting experiments on artificial and real-world datasets. Moreover, an application on the high-dimensional machine learning task of handwritten alphabet recognition is introduced. [ABSTRACT FROM AUTHOR]

Proteomic analysis of extracellular vesicles presents several challenges due to the unique nature of these small membrane-bound structures. Alternative analyses could reveal outcomes hidden from standard statistics to explore and develop potential new biological hypotheses that may have been overlooked during the initial evaluation of the data. An analysis sequence focusing on deviating protein expressions from donors' primary cells was performed, leveraging machine-learning techniques to analyze small datasets, and it has been applied to evaluate extracellular vesicles' protein content gathered from mesenchymal stem cells cultured on bioactive glass discs doped or not with metal ions. The goal was to provide additional opportunities for detecting details between experimental conditions that are not entirely revealed with classic statistical inference, offering further insights regarding the experimental design and assisting the researchers in interpreting the outcomes. The methodology extracted a set of EV-related proteins whose differences between conditions could be partially explainable with statistics, suggesting the presence of other factors involved in the bioactive glasses' interactions with tissues. Outlier identification of extracellular vesicles' protein expression levels related to biomaterial preparation was instrumental in improving the interpretation of the experimental outcomes. [ABSTRACT FROM AUTHOR]

The only cases where exact distributions of estimates are known is for samples from exponential families, and then only for special functions of the parameters. So statistical inference was traditionally based on the asymptotic normality of estimates. To improve on this we need the Edgeworth expansion for the distribution of the standardised estimate. This is an expansion in n − 1 / 2 about the normal distribution, where n is typically the sample size. The first few terms of this expansion were originally given for the special case of a sample mean. In earlier work we derived it for any standard estimate, hugely expanding its application. We define an estimate w ^ of an unknown vector w in R p , as a standard estimate, if E w ^ → w as n → ∞ , and for r ≥ 1 the rth-order cumulants of w ^ have magnitude n 1 − r and can be expanded in n − 1. Here we present a significant extension. We give the expansion of the distribution of any smooth function of w ^ , say t (w ^) in R q , giving its distribution to n − 5 / 2 . We do this by showing that t (w ^) , is a standard estimate of t (w) . This provides far more accurate approximations for the distribution of t (w ^) than its asymptotic normality. [ABSTRACT FROM AUTHOR]

In many real-life scenarios, one variable is observed only if the other concomitant variable or the set of concomitant variables (in the multivariate scenario) is truncated from below, above, or from a two-sided approach. Hidden truncation models have been applied to analyze data when bivariate or multivariate observations are subject to some form of truncation. While the statistical inference for hidden truncation models (truncation from above) under the frequentist and the Bayesian paradigms has been adequately discussed in the literature, the estimation of a two-sided hidden truncation model under the Bayesian framework has not yet been discussed. In this paper, we consider the Bayesian inference for a general two-sided hidden truncation model based on the Arnold–Strauss bivariate exponential distribution. In addition, a Bayesian model selection approach based on the Bayes factor to select between models without truncation, with truncation from below, from above, and two-sided truncation is also explored. An extensive simulation study is carried out for varying parameter choices under the conjugate prior set-up. For illustrative purposes, a real-life dataset is re-analyzed to demonstrate the applicability of the proposed methodology. [ABSTRACT FROM AUTHOR]

Generalized Pareto distribution (GPD), an asymmetrical distribution, primarily models exceedances over a high threshold in many applications. Within the peaks-over-threshold (POT) framework, we consider a new GPD parameter estimation method to estimate a common tail risk measure, the value at risk (VaR). The proposed method is more suitable for the POT framework and makes full use of data information. Specifically, our estimation method builds upon the generalized probability weighted moments method and integrates it with the nonlinear weighted least squares method. We use exceedances for the GPD, minimizing the sum of squared differences between the sample and population moments of a function of GPD random variables. At the same time, the proposed estimator uses three iterations and assigns weight to further improving the estimated performance. Under Monte Carlo simulations and with a real heavy-tailed dataset, the simulation results show the advantage of the newly proposed estimator, particularly when VaRs are at high confidence levels. In addition, by simulating other heavy-tailed distributions, our method still exhibits good performance in estimating misjudgment distributions. [ABSTRACT FROM AUTHOR]

Simple Summary: This study aimed to understand the language challenges faced by English-speaking animal professionals when communicating with Hispanic/Spanish-speaking animal caretakers. A survey was conducted among bilingual and non-Spanish-speaking professionals, revealing that non-Spanish-speaking individuals struggled with both written and oral communication compared to bilingual counterparts. Female professionals exhibited differences in their responses, particularly regarding the importance of certain aspects of the Spanish language while interacting with Hispanic caretakers. These findings highlight communication gaps that need to be addressed to improve interactions with on-farm Hispanic/Spanish-speaking animal caretakers and consequently contribute to enhancing animal health, welfare, and production. This study focused on assessing the language needs of English-speaking animal professionals in their interactions with Hispanic/Spanish-speaking animal caretakers. A survey was administered to a target audience of non-Spanish speaking and bilingual animal professionals to identify communication gaps while interacting with Hispanic/Spanish-speaking animal caretakers. The data was analyzed with descriptive and inferential statistics, including ordinal regression analyses to examine the impact of demographic variables on respondents' answer choices. The results showed that English-speaking professionals struggled with written and oral communication, which differed compared to bilingual professionals (p < 0.05). Additionally, responses of female professionals varied regarding the aspects of Spanish necessary for interacting with Hispanic/Spanish-speaking animal caretakers, as well as the topics likely to be addressed when agriculture professionals communicate with animal caretakers (p < 0.05). Communication difficulties in the oral medium for both oral receptive skills (listening) and oral productive skills (speaking) were reported as the major barriers that animal professionals need to overcome in their attempt to communicate with the Hispanic/Spanish-speaking workforce in farm settings. This emphasizes the need to address oral communication barriers, and to a lesser degree, the development of reading and writing skills. The topics: typical clinical signs of illness, euthanasia, treatment—drugs, and identification of sick or injured animals were identified as the most likely to be addressed during on-farm interactions. These findings indicate that there are gaps in communication that need to be overcome to improve communication with on-farm Hispanic/Spanish-speaking animal caretakers and consequently contribute to enhancing animal health, welfare, and production. [ABSTRACT FROM AUTHOR]

In this paper, the statistical inference of the partially linear varying coefficient quantile regression model is studied under random missing responses. A two-stage estimation procedure is developed to estimate the parametric and nonparametric components involved in the model. Furthermore, the asymptotic properties of the estimators obtained are established under some mild regularity conditions. In addition, the empirical log-likelihood ratio statistic based on imputation is proposed, and it is proven that this statistic obeys the standard Chi-square distribution; thus, the empirical likelihood confidence interval of the parameter component of the model is constructed. Finally, simulation results show that the proposed estimation method is feasible and effective. [ABSTRACT FROM AUTHOR]

The safety and reliability of undivided two-way highway–rail grade crossings (HRGCs) are of paramount importance in transportation systems. Utilizing crash data from the Federal Railroad Administration between 2020 and 2021, this study aims to predict crash injury severity outcomes and investigate various factors influencing injury severities. The χ2 test was first used to select variables that were significantly associated with injury outcomes. By employing the eXtreme Gradient Boosting (XGBoost) model and interpretable SHapley Additive exPlanations (SHAP), a cross-category safety assessment that offers an evidence-based hierarchy and statistical inference of risk factors associated with crashes, crossings, vehicles, drivers, and environment was provided for killed, injured, and uninjured outcomes. Some significant predictors overlapped between the killed and injured models, such as old driver, driver was in vehicle, main track, went around the gate, adverse crossing surface, and truck, while the other different significant factors revealed that the model could distinguish between different severity levels. Additionally, the results suggested that the model has varying performances in predicting different injury severities, with the killed model having the highest accuracy of 93.36%. The SHAP dependency plots for the top three features also ensure reliable predictions and inform potential interventions aimed at strengthening traffic safety and risk management practices, such as enhanced warning systems and targeted educational campaigns for older drivers. [ABSTRACT FROM AUTHOR]

The paper makes a case that the current discussions on replicability and the abuse of significance testing have overlooked a more general contributor to the untrustworthiness of published empirical evidence, which is the uninformed and recipe-like implementation of statistical modeling and inference. It is argued that this contributes to the untrustworthiness problem in several different ways, including [a] statistical misspecification, [b] unwarranted evidential interpretations of frequentist inference results, and [c] questionable modeling strategies that rely on curve-fitting. What is more, the alternative proposals to replace or modify frequentist testing, including [i] replacing p-values with observed confidence intervals and effects sizes, and [ii] redefining statistical significance, will not address the untrustworthiness of evidence problem since they are equally vulnerable to [a]–[c]. The paper calls for distinguishing between unduly data-dependant 'statistical results', such as a point estimate, a p-value, and accept/reject H 0 , from 'evidence for or against inferential claims'. The post-data severity (SEV) evaluation of the accept/reject H 0 results, converts them into evidence for or against germane inferential claims. These claims can be used to address/elucidate several foundational issues, including (i) statistical vs. substantive significance, (ii) the large n problem, and (iii) the replicability of evidence. Also, the SEV perspective sheds light on the impertinence of the proposed alternatives [i]–[iii], and oppugns [iii] the alleged arbitrariness of framing H 0 and H 1 which is often exploited to undermine the credibility of frequentist testing. [ABSTRACT FROM AUTHOR]

Parameter estimation is an important component of statistical inference, and how to improve the accuracy of parameter estimation is a key issue in research. This paper proposes a linear Bayesian estimation for estimating parameters in a misrecorded Poisson distribution. The linear Bayesian estimation method not only adopts prior information but also avoids the cumbersome calculation of posterior expectations. On the premise of ensuring the accuracy and stability of computational results, we derived the explicit solution of the linear Bayesian estimation. Its superiority was verified through numerical simulations and illustrative examples. [ABSTRACT FROM AUTHOR]

In a previous work, we introduced, in the context of gravitational wave science, an initial study on an automated domain-decomposition approach for a reduced basis through hp-greedy refinement. The approach constructs local reduced bases of lower dimensionality than global ones, with the same or higher accuracy. These "light" local bases should imply both faster evaluations when predicting new waveforms and faster data analysis, particularly faster statistical inference (the forward and inverse problems, respectively). In this approach, however, we have previously found important dependence on several hyperparameters, which do not appear in a global reduced basis. This naturally leads to the problem of hyperparameter optimization (HPO), which is the subject of this paper. Here, we compare the efficiency of the Bayesian approach against grid and random searches, which are two order of magnitude slower. Then, we tackle the problem of HPO through Bayesian optimization.We find that, for the cases studied here of gravitational waves from the collision of two spinning but non-precessing black holes, for the same accuracy, local hp-greedy reduced bases with HPO have a lower dimensionality of up to 4×, depending on the desired accuracy. This factor should directly translate into a parameter estimation speedup in the context of reduced order quadratures, for instance. Such acceleration might help in the near real-time requirements for electromagnetic counterparts of gravitational waves from compact binary coalescences. The code developed for this project is available open source from public repositories. This paper is an invited contribution to the Special Issue "Recent Advances in Gravity: A Themed Issue in Honor of Prof. Jorge Pullin on his 60th Anniversary". [ABSTRACT FROM AUTHOR]

Partially linear models find extensive application in biometrics, econometrics, social sciences, and various other fields due to their versatility in accommodating both parametric and nonparametric elements. This study aims to establish statistical inference for the parametric component effects within these models, employing a nonparametric empirical likelihood approach. The proposed method involves a projection step to eliminate the nuisance nonparametric component and utilizes an empirical-likelihood-based technique, along with the Bartlett correction, to enhance the coverage probability of the confidence interval for the parameter of interest. This method demonstrates robustness in handling normally and non-normally distributed errors. The proposed empirical likelihood ratio statistic converges to a limiting chi-square distribution under certain regulations. Simulation studies demonstrate that this method provides better inference in terms of coverage probabilities compared to the conventional normal-approximation-based method. The proposed method is illustrated by analyzing the Boston housing data from a real study. [ABSTRACT FROM AUTHOR]

This article presents an extended distribution that builds upon the exponential distribution. This extension is based on a scale mixture between the exponential and beta distributions. By utilizing this approach, we obtain a distribution that offers increased flexibility in terms of the kurtosis coefficient. We explore the general density, properties, moments, asymmetry, and kurtosis coefficients of this distribution. Statistical inference is performed using both the moments and maximum likelihood methods. To show the performance of this new model, it is applied to a real dataset with atypical observations. The results indicate that the new model outperforms two other extensions of the exponential distribution. [ABSTRACT FROM AUTHOR]

In this article we introduce an extension of the Akash distribution. We use the slash methodology to make the kurtosis of the Akash distribution more flexible. We study the general probability density function of this new model, some properties, moments, skewness and kurtosis coefficients. Statistical inference is performed using the methods of moments and maximum likelihood via the EM algorithm. A simulation study is carried out to observe the behavior of the maximum likelihood estimator. An application to a real data set with high kurtosis is considered, where it is shown that the new distribution fits better than other extensions of the Akash distribution. [ABSTRACT FROM AUTHOR]

Purpose: Cancer survivors can experience symptoms such as fatigue, pain and distress that persist for many months following treatment. These enduring symptoms often impact on participation in self-care activities, returning to school and/or work, and leisure and social activities. Self-management support is increasingly recognised as a core aspect of cancer survivorship care to reduce the impact of persistent symptoms. The purpose of this study was to examine the feasibility and potential effectiveness of a group-based self-management intervention, OptiMal, to improve the physical and psychological health of cancer survivors. OptiMal is a six-week intervention comprising weekly sessions on fatigue, stress and physical activity, diet and effective communication strategies. Methods: A feasibility randomised control trial was undertaken. Individuals up to two years after cancer treatment were randomised to OptiMal or usual care. Feasibility was examined through recruitment and retention metrics. Potential effectiveness was tested through patient-reported outcomes collected at baseline and three months post-intervention. Descriptive and inferential statistics were used to analyse study data. Results: Recruitment for this study was 32.5% (80/246 eligible individuals) with 77.5% retention at three-month follow-up (82.5% for intervention group and 72.5% for control group). Of those who attended the intervention, 19 (73%) attended all OptiMal sessions, indicating high adherence to the intervention. The majority of participants had breast cancer and were between 12 and 24 months post-treatment. The intervention group (n = 29) had statistically significant greater improvements in anxiety (p = 0.04) and health-related quality of life (health index score: p = 0.023, visual analogue score: p = 0.035) at three months post-intervention than the control group. Conclusions: Recruitment and retention in this study was similar to other cancer trials and the high adherence rate indicates that OptiMal is an acceptable self-management intervention for cancer survivors and warrants further investigation. OptiMal is intended to address symptoms reported across different cancer types. However, a limitation of this study was that the majority of participants had breast cancer, and therefore, generalisability of findings cannot be assumed for other cancer types. Future studies of OptiMal therefore need to use different strategies to recruit survivors of other cancer types. [ABSTRACT FROM AUTHOR]

In this paper, we extend the Lomax–Rayleigh distribution to increase its kurtosis. The construction of this distribution is based on the idea of the Slash distribution, that is, its representation is based on the quotient of two independent random variables, one being a random variable with a Lomax–Rayleigh distribution and the other a beta (q , 1) . Based on the representation of this family, we study its basic properties, such as moments, coefficients of skewness, and kurtosis. We perform statistical inference using the methods of moments and maximum likelihood. To illustrate this methodology, we apply it to two real data sets. [ABSTRACT FROM AUTHOR]

This paper studies the estimation and inference of a partially linear varying coefficient spatial autoregressive panel data model with fixed effects. By means of the basis function approximations and the instrumental variable methods, we propose a two-stage least squares estimation procedure to estimate the unknown parametric and nonparametric components, and meanwhile study the asymptotic properties of the proposed estimators. Together with an empirical log-likelihood ratio function for the regression parameters, which follows an asymptotic chi-square distribution under some regularity conditions, we can further construct accurate confidence regions for the unknown parameters. Simulation studies show that the finite sample performance of the proposed methods are satisfactory in a wide range of settings. Lastly, when applied to the public capital data, our proposed model can also better reflect the changing characteristics of the US economy compared to the parametric panel data models. [ABSTRACT FROM AUTHOR]

We study the excess minimum risk in statistical inference, defined as the difference between the minimum expected loss when estimating a random variable from an observed feature vector and the minimum expected loss when estimating the same random variable from a transformation (statistic) of the feature vector. After characterizing lossless transformations, i.e., transformations for which the excess risk is zero for all loss functions, we construct a partitioning test statistic for the hypothesis that a given transformation is lossless, and we show that for i.i.d. data the test is strongly consistent. More generally, we develop information-theoretic upper bounds on the excess risk that uniformly hold over fairly general classes of loss functions. Based on these bounds, we introduce the notion of a δ -lossless transformation and give sufficient conditions for a given transformation to be universally δ -lossless. Applications to classification, nonparametric regression, portfolio strategies, information bottlenecks, and deep learning are also surveyed. [ABSTRACT FROM AUTHOR]

Recently, there has been a lot of interest in comparative life testing for items under jointly censored schemes for products from multiple production lines. The inverse Weibull distribution (IWD) is commonly used in life testing and reliability theory. In this paper, we address the problem of statistical inference from comparative inverse Weibull distributions under joint samples. An adaptive type-II hybrid progressive censoring scheme (HPCS) is used to save the balance between the ideal test time and the number of observed failures. Under the adaptive type-II HPCS, unknown parameters of the inverse Weibull populations are estimated using both maximum likelihood and Bayesian approaches. Asymptotic confidence intervals are established using the observed Fisher information matrix and bootstrap confidence intervals. We suggest using Markov chain Monte Carlo (MCMC) techniques to compute credible intervals under independent gamma priors. Using Monte Carlo simulations, all theoretical conclusions are tested and contrasted. For illustration purposes, an actual sample from comparative populations is analysed. [ABSTRACT FROM AUTHOR]

The joint censoring technique becomes crucial when the study's aim is to assess the comparative advantages of products concerning their service times. In recent years, there has been a growing interest in progressive censoring as a means to reduce both cost and experiment duration. This article delves into the realm of statistical inference for the three-parameter Burr-XII distribution using a joint progressive Type II censoring approach applied to two separate samples. We explore both maximum likelihood and Bayesian methods for estimating model parameters. Furthermore, we derive approximate confidence intervals based on the observed information matrix and employ four bootstrap methods to obtain confidence intervals. Bayesian estimators are presented for both symmetric and asymmetric loss functions. Since closed-form solutions for Bayesian estimators are unattainable, we resort to the Markov chain Monte Carlo method to compute these estimators and the corresponding credible intervals. To assess the performance of our estimators, we conduct extensive simulation experiments. Finally, to provide a practical illustration, we analyze a real dataset. [ABSTRACT FROM AUTHOR]

In many practical applications, such as the studies of financial and biomedical data, the response variable usually is positive, and the commonly used criteria are based on absolute errors, which is not desirable. Rather, the relative errors are more of concern. We consider statistical inference for a partially linear multiplicative regression model when covariates in the linear part are measured with error. The simulation–extrapolation (SIMEX) estimators of parameters of interest are proposed based on the least product relative error criterion and B-spline approximation, where two kinds of relative errors are both introduced and the symmetry emerges in the loss function. Extensive simulation studies are conducted and the results show that the proposed method can effectively eliminate the bias caused by the measurement errors. Under some mild conditions, the asymptotic normality of the proposed estimator is established. Finally, a real example is analyzed to illustrate the practical use of our proposed method. [ABSTRACT FROM AUTHOR]

Overlapping coefficients (OVL) are commonly used to estimate the similarity between populations in terms of their density functions. In this paper, we consider Pianka's overlap coefficient for two exponential populations. The methods for statistical inference of Pianka's coefficient are presented. The bias and mean square error (MSE) of the maximum likelihood estimator (MLE) and the Bayes estimator of Pianka's overlap coefficient are investigated by simulation. Confidence intervals for Pianka's overlap measure are constructed. [ABSTRACT FROM AUTHOR]

This retrospective study aims to investigate the impact of cone-beam computed tomography (CBCT) viewing parameters such as contrast, slice thickness, and sharpness on the identification of the inferior alveolar nerve (IAC). A total of 25 CBCT scans, resulting in 50 IACs, were assessed by two investigators using a three-score system (good, average, and poor) on cross-sectional images. Slice thicknesses of 0.25 mm, 0.5 mm, and 1 mm were tested, along with varying sharpness (0, 6, 8, and 10) and contrast (0, 400, 800, and 1200) settings. The results were statistically analyzed to determine the optimal slice thickness for improved visibility of IAC, followed by evaluating the influence of sharpness and contrast using the optimal thickness. The identified parameters were then validated by performing semi-automated segmentation of the IACs and structure overlapping to evaluate the mean distance. Inter-rater and intra-rater reliability were assessed using Kappa statistics, and inferential statistics used Pearson's Chi-square test. Inter-rater and intra-rater reliability for all parameters were significant, ranging from 69% to 83%. A slice thickness of 0.25 mm showed consistently "good" visibility (80%). Sharpness values of zero and contrast values of 1200 also demonstrated high frequencies of "good" visibility. Overlap analysis resulted in an average mean distance of 0.295 mm and a standard deviation of 0.307 mm across all patients' sides. The study revealed that a slice thickness of 0.25 mm, zero sharpness value, and higher contrast value of 1200 improved the visibility and accuracy of IAC segmentation in CBCT scans. The individual patient's characteristics, such as anatomical variations, decreased bone density, and absence of canal walls cortication, should be considered when using these parameters. [ABSTRACT FROM AUTHOR]

We develop a new model for spatio-temporal data. More specifically, a graph penalty function is incorporated in the cost function in order to estimate the unknown parameters of a spatio-temporal mixed-effect model based on a generalized linear model. This model allows for more flexible and general regression relationships than classical linear ones through the use of generalized linear models (GLMs) and also captures the inherent structural dependencies or relationships of the data through this regularization based on the graph Laplacian. We use a publicly available dataset from the National Centers for Environmental Information (NCEI) in the United States of America and perform statistical inferences of future CO 2 emissions in 59 counties. We empirically show how the proposed method outperforms widely used methods, such as the ordinary least squares (OLS) and ridge regression for this challenging problem. [ABSTRACT FROM AUTHOR]

In scientific problems, an appropriate statistical model often involves a large number of canonical parameters. Often times, the quantities of scientific interest are real-valued functions of these canonical parameters. Statistical inference for a specified function of the canonical parameters can be carried out via the Bayesian approach by simply using the posterior distribution of the specified function of the parameter of interest. Frequentist inference is usually based on the profile likelihood for the parameter of interest. When the likelihood function is analytical, computing the profile likelihood is simply a constrained optimization problem with many numerical algorithms available. However, for hierarchical models, computing the likelihood function and hence the profile likelihood function is difficult because of the high-dimensional integration involved. We describe a simple computational method to compute profile likelihood for any specified function of the parameters of a general hierarchical model using data doubling. We provide a mathematical proof for the validity of the method under regularity conditions that assure that the distribution of the maximum likelihood estimator of the canonical parameters is non-singular, multivariate, and Gaussian. [ABSTRACT FROM AUTHOR]

Survey sampling has a wide range of applications in biomedical, meteorological, stock exchange, marketing, and agricultural research based on data collected through sample surveys or experimentation. The collected set of information may have a fuzzy nature, be indeterminate, and be summarized by a fuzzy number rather than a crisp value. The neutrosophic statistics, a generalization of fuzzy statistics and classical statistics, deals with the data that have some degree of indeterminacy, imprecision, and fuzziness. In this article, we introduce a fuzzy decision-making approach for deciding a sample size under a fuzzy measurement cost modeled by an intuitionistic fuzzy cost function. Our research introduces neutrosophic ratio-type estimators for estimating the population mean of the neutrosophic study variable Y N ∈ [ Y L , Y U ] utilizing all the indeterminate values of the neutrosophic auxiliary variable X N ∈ [ X L , X U ] rather than only the extreme values X L and X U . Three simulation studies are carried out to explain the proposed methods of parameter estimation, sample size determination, and efficiency comparison. The results reveal that the proposed neutrosophic class of estimators produces more accurate and precise estimates of the neutrosophic population mean than the existing neutrosophic estimators in simple random sampling, which is the ultimate goal of inferential statistics. [ABSTRACT FROM AUTHOR]

This study addresses the issue of estimating the shape parameter of the inverted exponentiated Rayleigh distribution, along with the assessment of reliability and failure rate, by utilizing Type-I progressive hybrid censored data. The study explores the estimators based on maximum likelihood, Bayes, and empirical Bayes methodologies. Additionally, the study focuses on the development of Bayes and empirical Bayes estimators with balanced loss functions. A concrete example based on actual data from the field of medicine is used to illustrate the theoretical insights provided in this study. Monte Carlo simulations are employed to conduct numerical comparisons and evaluate the performance and accuracy of the estimation methods. [ABSTRACT FROM AUTHOR]

Pediatric Brain Tumor Survivors (PBTS) often experience social, academic and employment difficulties during aftercare. Despite their needs, they often do not use the services available to them. Following a previous qualitative study, we formulated solutions to help support PBTS return to daily activities after treatment completion. The present study aims to confirm and prioritize these solutions with a larger sample. We used a mixed-methods survey with 68 participants (43 survivors, 25 parents, PBTS' age: 15–39 years). Firstly, we collected information about health condition, and school/work experience in aftercare. Then, we asked participants to prioritize the previously identified solutions using Likert scales and open-ended questions. We used descriptive and inferential statistics to analyze data, and qualitative information to support participants' responses. Participants prioritized the need for evaluation, counseling, and follow-up by health professionals to better understand their post-treatment needs, obtain help to access adapted services, and receive information about resources at school/work. Responses to open-ended questions highlighted major challenges regarding the implementation of professionals' recommendations at school/work and the need for timely interventions. These results will help refine solutions for PBTS and provide key elements for future implementation. Translating these priorities into action will need further work involving professionals and decision makers. [ABSTRACT FROM AUTHOR]

In this work, we study the possibility of using a new non-homogeneous stochastic diffusion process based on the Rayleigh density function to model the evolution of the active cases of COVID-19 in Morocco. First, the main probabilistic characteristics and analytic expression of the proposed process are obtained. Next, the parameters of the model are estimated by the maximum likelihood methodology. This estimation and the subsequent statistical inference are based on the discrete observation of the variable x (t) "number of active cases of COVID-19 in Morocco" by using the data for the period of 28 January to 4 March 2022. Then, we analyze the mean functions by using simulated data for fit and forecast purposes. Finally, we explore the illustration of using this new process to fit and forecast the active cases of COVID-19 data. [ABSTRACT FROM AUTHOR]

Recent independent observations using several different telescope systems and analysis methods have provided evidence of parity violation between the numbers of galaxies that spin in opposite directions. On the other hand, other studies argue that no parity violation can be identified. This paper provides detailed analysis, statistical inference, and reproduction of previous reports that show no preferred spin direction. Code and data used for the reproduction are publicly available. The results show that the data used in all of these studies agree with the observation of a preferred direction as observed from Earth. In some of these studies, the datasets were too small, or the statistical analysis was incomplete. In other papers, the results were impacted by experimental design decisions that led directly to showing nonpreferred direction. In some of these cases, these decisions were not stated in the papers but were revealed after further investigation in cases where the reproduction of the work did not match the results reported in the papers. These results show that the data used in all of these previous studies, in fact, agree with the contention that galaxies as observed from Earth have a preferred spin direction, and the distribution of galaxy spin directions as observed from Earth forms a cosmological-scale dipole axis. This study also shows that the reason for the observations is not necessarily an anomaly in the large-scale structure, and can also be related to internal structure of galaxies. [ABSTRACT FROM AUTHOR]

Response times (RT) distributions are routinely used by psychologists and neuroscientists in the assessment and modeling of human behavior and cognition. The statistical properties of RT distributions are valuable in uncovering unobservable psychological mechanisms. A potentially important statistical aspect of RT distributions is their entropy. However, to date, no valid measure of entropy on RT distributions has been developed, mainly because available extensions of discrete entropy measures to continuous distributions were fraught with problems and inconsistencies. The present work takes advantage of the cumulative residual entropy (CRE) function—a well-known differential entropy measure that can circumvent those problems. Applications of the CRE to RT distributions are presented along with concrete examples and simulations. In addition, a novel measure of instantaneous CRE is developed that captures the rate of entropy reduction (or information gain) from a stimulus as a function of processing time. Taken together, the new measures of entropy in RT distributions proposed here allow for stronger statistical inferences, as well as motivated theoretical interpretations of psychological constructs such as mental effort and processing efficiency. [ABSTRACT FROM AUTHOR]

In this article, we introduce the Kavya–Manoharan generalized inverse Kumaraswamy (KM-GIKw) distribution, which can be presented as an improved version of the generalized inverse Kumaraswamy distribution with three parameters. It contains numerous referenced lifetime distributions of the literature and a large panel of new ones. Among the essential features and attributes covered in our research are quantiles, moments, and information measures. In particular, various entropy measures (Rényi, Tsallis, etc.) are derived and discussed numerically. The adaptability of the KM-GIKw distribution in terms of the shapes of the probability density and hazard rate functions demonstrates how well it is able to fit different types of data. Based on it, an acceptance sampling plan is created when the life test is truncated at a predefined time. More precisely, the truncation time is intended to represent the median of the KM-GIKw distribution with preset factors. In a separate part, the focus is put on the inference of the KM-GIKw distribution. The related parameters are estimated using the Bayesian, maximum likelihood, and maximum product of spacings methods. For the Bayesian method, both symmetric and asymmetric loss functions are employed. To examine the behaviors of various estimates based on criterion measurements, a Monte Carlo simulation research is carried out. Finally, with the aim of demonstrating the applicability of our findings, three real datasets are used. The results show that the KM-GIKw distribution offers superior fits when compared to other well-known distributions. [ABSTRACT FROM AUTHOR]

A bimodal double log-normal distribution on the real line is proposed using the random sign mixture transform. Its associated statistical inferences are derived. Its parameters are estimated by the maximum likelihood method. The performance of the estimators and the corresponding confidence intervals is checked by simulation studies. Application of the proposed distribution to a real data set from a DNA microarray is presented. [ABSTRACT FROM AUTHOR]

Bertrand's paradox is a problem in geometric probability that has resisted resolution for more than one hundred years. Bertrand provided three seemingly reasonable solutions to his problem — hence the paradox. Bertrand's paradox has also been influential in philosophical debates about frequentist versus Bayesian approaches to statistical inference. In this paper, the paradox is resolved (1) by the clarification of the primary variate upon which the principle of maximum entropy is employed and (2) by imposing constraints, based on a mathematical analysis, on the random process for any subsequent nonlinear transformation to a secondary variable. These steps result in a unique solution to Bertrand's problem, and this solution differs from the classic answers that Bertrand proposed. It is shown that the solutions proposed by Bertrand and others reflected sampling processes that are not purely random. It is also shown that the same two steps result in the resolution of the Bing–Fisher problem, which has to do with the selection of a consistent prior for Bayesian inference. The resolution of Bertrand's paradox and the Bing–Fisher problem rebuts philosophical arguments against the Bayesian approach to statistical inference, which were based on those two ostensible problems. [ABSTRACT FROM AUTHOR]

High-dimensional measurement error data are becoming more prevalent across various fields. Research on measurement error regression models has gained momentum due to the risk of drawing inaccurate conclusions if measurement errors are ignored. When the dimension p is larger than the sample size n, it is challenging to develop statistical inference methods for high-dimensional measurement error regression models due to the existence of bias, nonconvexity of the objective function, high computational cost and many other difficulties. Over the past few years, some works have overcome the aforementioned difficulties and proposed several novel statistical inference methods. This paper mainly reviews the current development on estimation, hypothesis testing and variable screening methods for high-dimensional measurement error regression models and shows the theoretical results of these methods with some directions worthy of exploring in future research. [ABSTRACT FROM AUTHOR]

A new two-parameter statistical model, obtained by compounding the generalized-exponential and exponential distributions, called the PRC lifetime model, is explored in this paper. This model can be easily linked to other well-known six-lifetime models; namely the exponential, log-logistic, Burr, Pareto and generalized Pareto models. Adaptive progressively hybrid Type-II censored strategy, used to increase the efficiency of statistical inferential results and save the total duration of a test, has become widely used in various sectors such as medicine, biology, engineering, etc. Via maximum likelihood and Bayes inferential methodologies, given the presence of such censored data, the challenge of estimating the unknown parameters and some reliability time features, such as reliability and failure rate functions, of the PRC model is examined. The Markov-Chain Monte Carlo sampler, when the model parameters are assumed to have independent gamma density priors, is utilized to produce the Bayes' infer under the symmetric (squared-error) loss of all unknown subjects. Asymptotic confidence intervals as well as the highest posterior density intervals of the unknown parameters and the unknown reliability indices are also created. An extensive Monte Carlo simulation is implemented to investigate the accuracy of the acquired point and interval estimators. Four various optimality criteria, to select the best progressive censored design, are used. To demonstrate the applicability and feasibility of the proposed model in a real-world scenario, two data sets from the engineering sector; one based on industrial devices and the other on aircraft windshield, are analyzed. Numerical evaluations showed that the PRC model furnishes a superior fit compared to seven other models in the literature, including: alpha-power exponential, log-logistic, Nadarajah–Haghighi, generalized-exponential, Weibull, gamma and exponential lifetime distributions. The findings demonstrate that, in order to obtain the necessary estimators, the Bayes' paradigm via Metropolis–Hastings sampler is recommended compared to its competitive likelihood approach. [ABSTRACT FROM AUTHOR]

Inspired by the development in modern data science, a shift is increasingly visible in the foundation of statistical inference, away from a real space, where random variables reside, toward a nonmetrized and nonordinal alphabet, where more general random elements reside. While statistical inferences based on random variables are theoretically well supported in the rich literature of probability and statistics, inferences on alphabets, mostly by way of various entropies and their estimation, are less systematically supported in theory. Without the familiar notions of neighborhood, real or complex moments, tails, et cetera, associated with random variables, probability and statistics based on random elements on alphabets need more attention to foster a sound framework for rigorous development of entropy-based statistical exercises. In this article, several basic elements of entropic statistics are introduced and discussed, including notions of general entropies, entropic sample spaces, entropic distributions, entropic statistics, entropic multinomial distributions, entropic moments, and entropic basis, among other entropic objects. In particular, an entropic-moment-generating function is defined and it is shown to uniquely characterize the underlying distribution in entropic perspective, and, hence, all entropies. An entropic version of the Glivenko–Cantelli convergence theorem is also established. [ABSTRACT FROM AUTHOR]

When conducting reliability studies, the progressive first-failure censoring (PFFC) method is useful in situations in which the units of the life testing experiment are separated into groups consisting of k units each with the intention of seeing only the first failure in each group. Using progressive first-failure censored samples, the statistical inference for the parameters, reliability, and hazard functions of the extended Rayleigh distribution (ERD) are investigated in this study. The asymptotic normality theory of maximum likelihood estimates (MLEs) is used in order to acquire the maximum likelihood estimates (MLEs) together with the asymptotic confidence intervals (Asym. CIs). Bayesian estimates (BEs) of the parameters and the reliability functions under different loss functions may be produced by using independent gamma informative priors and non-informative priors. The Markov chain Monte Carlo (MCMC) approach is used so that Bayesian computations are performed with ease. In addition, the MCMC method is used in order to create credible intervals (Cred. CIs) for the parameters, which may be used for either informative or non-informative priors. Additionally, computations for the reliability functions are carried out. A Monte Carlo simulation study is carried out in order to provide a comparison of the behaviour of the different estimations that were created for this work. At last, an actual data set is dissected for the purpose of providing an example. [ABSTRACT FROM AUTHOR]

Today, the reliability or quality practitioner always aims to shorten testing duration and reduce testing costs without neglecting efficient statistical inference. So, a generalized progressively Type-II hybrid censored mechanism has been developed in which the experimenter prepays for usage of the testing facility for T units of time. This paper investigates the issue of estimating the model parameter, reliability, and hazard rate functions of the Maxwell–Boltzmann distribution in the presence of generalized progressive Type-II hybrid censored data by making use of the likelihood and Bayesian inferential methods. Using an inverse gamma prior distribution, the Bayes estimators of the same unknown parameters with respect to the most commonly squared-error loss are derived. Since the joint likelihood function is produced in complex form, following the Monte-Carlo Markov-chain idea, the Bayes' point estimators as well as the Bayes credible and highest posterior density intervals cannot be derived analytically, but they may be examined numerically. Via the normal approximation of the acquired maximum likelihood and log-maximum-likelihood estimators, the approximate confidence interval bounds of the unknown quantities are derived. Via comprehensive numerical comparisons, with regard to simulated root mean squared-error, mean relative absolute bias, average confidence length, and coverage probability, the actual behavior of the proposed estimation methodologies is examined. To illustrate how the offered methodologies may be used in real circumstances, two different applications, representing the failure time points of aircraft windscreens as well as the daily average wind speed in Cairo during 2009, are explored. Numerical evaluations recommend utilizing a Bayes model via the Metropolis-Hastings technique to produce samples from the posterior distribution to estimate any parameter of the Maxwell–Boltzmann distribution when collecting data from a generalized progressively Type-II hybrid censored mechanism. [ABSTRACT FROM AUTHOR]

This paper is an attempt to study the Xgamma–Weibull distribution using an adaptive progressive type-II censoring plan. This scheme effectively ensures that the experimental time does not exceed a predetermined time limit. Using two classical estimation methods—namely, maximum likelihood and maximum product of spacing—both point and interval estimations for the unknown model parameters, as well as some parameters of life—namely, reliability and hazard rate functions—were obtained. The asymptotic normality of both classical methods was used to determine the approximate confidence intervals for the various parameters. Based on the two conventional methodologies, Bayesian estimations were also investigated using the MCMC technique under the squared error loss function. In addition, the credible intervals of the different parameters were also obtained. To compare the performance of the various approaches, a thorough simulation study was carried out. Furthermore, we propose using several optimality criteria to select the best sampling technique. Finally, two real-world datasets were used to demonstrate how the suggested estimators and optimality criteria operate in real-world circumstances. [ABSTRACT FROM AUTHOR]

The data envelopment analysis is related to a non-parametric mathematical tool used to assess the relative efficiency of productive units. In different studies on productive efficiency, it is common to employ semi-parametric procedures in two stages to determine whether any exogenous factors of interest affect the performance of productive units. However, some of these procedures, particularly those based on conventional statistical inference, generate inconsistent estimates when dealing with incoherent data-generating processes. This inconsistency arises due to the efficiency scores being limited to the unit interval, and the estimated scores often exhibit serial correlation and have limited observations. To address such inconsistency, several strategies have been suggested, with the most well-known being an algorithm based on a parametric bootstrap procedure using the truncated normal distribution and its regression model. In this work, we present a modification of this algorithm that utilizes the beta distribution and its regression structure. The beta model allows for better accommodation of asymmetry in the data distribution. Our proposed algorithm introduces inferential characteristics that are superior to the original algorithm, resulting in a more statistically coherent data-generating process and improving the consistency property. We have conducted computational experiments that demonstrate the improved results achieved by our proposal. [ABSTRACT FROM AUTHOR]

Generalized logistic distribution, as the generalized form of the symmetric logistic distribution, plays an important role in reliability analysis. This article focuses on the statistical inference for the stress–strength parameter R = P (Y < X) of the generalized logistic distribution with the same and different scale parameters. Firstly, we use the frequentist method to construct asymptotic confidence intervals, and adopt the generalized inference method for constructing the generalized point estimators as well as the generalized confidence intervals. Then the generalized fiducial method is applied to construct the fiducial point estimators and the fiducial confidence intervals. Simulation results demonstrate that the generalized fiducial method outperforms other methods in terms of the mean square error, average length, and empirical coverage. Finally, three real datasets are used to illustrate the proposed methods. [ABSTRACT FROM AUTHOR]

In this paper, estimations of the parameter and acceleration factor of the Burr–Hatke exponential distribution in partially accelerated life tests under progressively type II censoring are investigated. By using typical maximum likelihood methods and the Bayesian method, point estimations of the distribution parameter and the acceleration factor are obtained. Based on the asymptotic normality and Delta method, approximate confidence intervals are established using the Fisher information matrix. The confidence intervals of the percentile bootstrap method are also evaluated. Comprehensive simulation tests are conducted to evaluate the estimations effects. A real dataset is studied by constructing a Burr–Hatke exponential model and analyzing the practicality and utility of parameter estimation. [ABSTRACT FROM AUTHOR]

Statistical modeling relies on a diverse range of statistical distributions, encompassing both univariate and multivariate distributions and/or discrete and continuous distributions. In the literature, numerous statistical methods have been proposed to approximate continuous distributions. The most commonly used approach is the use of the empirical distribution which is obtained from a random sample drawn from the distribution. However, it is very likely that the empirical distribution suffers from an accuracy problem when used to approximate the underlying distribution, especially if the sample size is not sufficient. In order to improve statistical inferences, various alternative forms of discrete approximation to the distribution were proposed in the literature. The choice of support points for the discrete approximation, known as Representative Points (RPs), becomes extremely important in terms of distribution approximations. In this paper we give a review of the three main methods for constructing RPs, namely based on the Monte Carlo method, the number-theoretic method (or quasi-Monte Carlo method), and the mean square error method, aiming to introduce such important methods to the statistical or mathematical community. Additional approaches for forming RPs are also briefly discussed. The review focuses on certain critical aspects such as theoretical properties and computational algorithms for constructing RPs. We also address the issue of the application of RPs through studying practical problems and provide evidence of RPs' advantages over random samples in approximating the distribution. [ABSTRACT FROM AUTHOR]

Comparative lifetime tests are extremely significant when the experimenters study the reliability of the comparative advantages of two products in competition. Considering joint type-II censoring, we deal with the inference when two product lines conform to two Gumbel type-II distributions. The maximum likelihood estimations of Gumbel type-II population parameters were obtained in the current research. An approximate confidence interval and a simultaneous confidence interval based on a Fisher information matrix were also constructed and compared with two bootstrap confidence intervals. Moreover, to evaluate the influence of the prior information, based on the concept of importance sampling, we calculated the Bayesian estimator together with their posterior risks in the case of gamma and non-informative priors under different loss functions. To compare the performances of the overall parameters' estimator, a Monte Carlo simulation was performed using numerical and graphical methods. Finally, a real data analysis was conducted to verify the accuracy of all the models and methods mentioned. [ABSTRACT FROM AUTHOR]

Generalized progressively Type-II hybrid strategy has been suggested to save both the duration and cost of a life test when the experimenter aims to score a fixed number of failed units. In this paper, using this mechanism, the maximum likelihood and Bayes inferential problems for unknown model parameters, in addition to both reliability, and hazard functions of the inverted exponentiated Rayleigh model, are acquired. Applying the observed Fisher data and delta method, the normality characteristic of the classical estimates is taken into account to derive confidence intervals for unknown parameters and several indice functions. In Bayes' viewpoint, through independent gamma priors against both symmetrical and asymmetrical loss functions, the Bayes estimators of the unknown quantities are developed. Because the Bayes estimators are acquired in complicated forms, a hybrid Monte-Carlo Markov-chain technique is offered to carry out the Bayes estimates as well as to create the related highest posterior density interval estimates. The precise behavior of the suggested estimation approaches is assessed using wide Monte Carlo simulation experiments. Two actual applications based on actual data sets from the mechanical and chemical domains are examined to show how the offered methodologies may be used in real current events. [ABSTRACT FROM AUTHOR]

This manuscript focuses on the statistical inference of the Kavya–Manoharan generalized exponential distribution under the generalized type-I progressive hybrid censoring sample (GTI-PHCS). Different classical approaches of estimation, such as maximum likelihood, the maximum product of spacing, least squares (LS), weighted LS, and percentiles under GTI-PHCS, are investigated. Based on the squared error and linear exponential loss functions, the Bayes estimates for the unknown parameters utilizing separate gamma priors under GTI-PHCS have been derived. Point and interval estimates of unknown parameters are developed. We carry out a simulation using the Monte Carlo algorithm to show the performance of the inferential procedures. Finally, real-world data collection is examined for illustration purposes. [ABSTRACT FROM AUTHOR]

Studying the ages of mobile phones is considered one of the most important things in the recent period in the field of shopping and modern technology. In this paper, we will consider that the ages of these phones follow a gamma distribution under progressive first-failure (PFF) censoring. All of the unknown parameters, as well as Shannon and Rényi entropies, were estimated for this distribution. The maximum likelihood (ML) approach was utilized to generate point estimates for the target parameters based on the considered censoring strategy. The asymptotic confidence intervals of the ML estimators (MLEs) of the targeted parameters were produced using the normal approximation to ML and log-transformed ML. We employed the delta method to approximate the variances of the Shannon and Rényi functions to obtain their asymptotic confidence intervals. Additionally, all parameter estimates utilized in this study were determined using the successful expectation–maximization (EM) method. The Metropolis–Hastings (MH) algorithm was applied to construct the Bayes estimators and related highest posterior density (HPD) credible intervals under various loss functions. Further, the proposed methodologies were contrasted using Monte Carlo simulations. Finally, the radio transceiver dataset was analyzed to substantiate our results. [ABSTRACT FROM AUTHOR]