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We study a nonparametric test procedure based on order statistics for testing the null hypothesis of equality of two continuous distributions. The exact null distribution of the proposed test statistic is obtained using an enumeration method and a novel combinatorial argument. A recurrence relation for the probability generating function and a sequential approach for computing the mean and variance of the distribution are given. Critical values and characteristics of the distribution for selected small sample sizes are presented. For the Lehmann alternative family, the exact power function of the new test is derived, and its power performance is examined. We also study the power performance of the proposed test under the location-shift and scale-shift alternatives using Monte Carlo simulations and observe its superior performance when compared to commonly used nonparametric tests under various scenarios. A generalization of the proposed procedure for unequal sample sizes is discussed. An illustrative example and some concluding remarks are provided. [ABSTRACT FROM AUTHOR]

In this study, we have presented a novel probabilistic model called the neutrosophic Burr-III distribution, designed for applications in neutrosophic surface analysis. Neutrosophic analysis allows for the incorporation of vague and imprecise information, reflecting the reality that many real-world problems involve ambiguous data. This ability to handle vagueness can lead to more robust and realistic models especially in situation where classical models fall short. We have also explored the neutrosophic Burr-III distribution in order to deal with the ambiguity and vagueness in the data where the classical Burr-III distribution falls short. This distribution offers valuable insights into various reliability properties, moment expressions, order statistics, and entropy measures, making it a versatile tool for analyzing complex data. To assess the practical relevance of our proposed distribution, we applied it to real-world data sets and compared its performance against the classical Burr-III distribution. The findings revealed that the neutrosophic Burr-III distribution outperformed than the classical Burr-III distribution in capturing the underlying data characteristics, highlighting its potential as a superior modeling toolin various fields. [ABSTRACT FROM AUTHOR]

In this article, extropy properties of the ranked set sample (RSS) when ranking is not perfect are considered. By deriving the expression for extropy of concomitant order statistic, the expression for extropy of RSS of the study variable Y in which an auxiliary variable X is used to rank the units in each set, under the assumption that (X , Y) follows Morgenstern family of distributions is obtained. The upper and lower bounds of extropy of RSS are obtained. The cumulative residual extropy of concomitant of order statistic and RSS arising from Morgenstern family of distributions are also obtained. The discrimination informations between the distribution of rth RSS statistic and the parent distribution are also obtained. [ABSTRACT FROM AUTHOR]

We introduced a flexible class of continuous distributions called the generalized Kavya-Manoharan-G (GKM-G) family. The GKM-G family extended the Kavya-Manoharan class and provided greater flexibility to the baseline models. The special sub-models of the GKM-G family are capable of modeling monotone and non-monotone failure rates including increasing, reversed J shape, decreasing, bathtub, modified bathtub, and upside-down bathtub. Some properties of the family were studied. The GKM-exponential (GKME) distribution was studied in detail. Eight methods of estimation were used for estimating the GKME parameters. The performance of the estimators was assessed by simulation studies under small and large samples. Furthermore, the flexibility of the twoparameter GKME distribution was explored by analyzing five real-life data applications from applied fields such as medicine, environment, and reliability. The data analysis showed that the GKME distribution outperforms other competing exponential models. [ABSTRACT FROM AUTHOR]

This paper aims to introduce a novel family of probability distributions by the well-known method of the T–X family of distributions. The proposed family is called a "Novel Generalized Exponent Power X Family" of distributions. A three-parameters special sub-model of the proposed method is derived and named a "Novel Generalized Exponent Power Weibull" distribution (NGEP-Wei for short). For the proposed family, some statistical properties are derived including the hazard rate function, moments, moment generating function, order statistics, residual life, and reverse residual life. The well-known method of estimation, the maximum likelihood estimation method is used for estimating the model parameters. Besides, a comprehensive Monte Carlo simulation study is conducted to assess the efficacy of this estimation method. Finally, the model selection criterion such as Akaike information criterion (AINC), the correct information criterion (CINC), the Bayesian information criterion (BINC), the Hannan–Quinn information criterion (HQINC), the Cramer–von-Misses (CRMI), and the ANDA (Anderson–Darling) are used for comparison purpose. The comparison of the NGEP-Wei with other rival distributions is made by Two COVID-19 data sets. In terms of performance, we show that the proposed method outperforms the other competing methods included in this study. [ABSTRACT FROM AUTHOR]

The laws of large numbers are studied from the arrays of asymmetrical Cauchy random variables. Some exact laws of large numbers are obtained for the k-th order statistics, including a weak law and a strong law. It turns out that the weak law cannot extend to a strong law. Our results extend some existing works for independent and dependent cases. [ABSTRACT FROM AUTHOR]

The microwave radiances are key observations especially over data sparse regions for operational data assimilation in numerical weather prediction (NWP). An often applied simplification is that these observations are used as point measurements, however, the satellite field-of-view may cover many grid points of high-resolution models. Therefore, we examine a solution in high-resolution data assimilation to better account for the spatial representation of the radiance observations. This solution is based on a footprint operator implemented and tested in the variational assimilation scheme of the AROME-Arctic (Application of Research to Operations at Mesoscale – Arctic) limited-area model. In this paper, the design and technical challenges of the microwave radiance footprint operator are presented. In particular, implementation strategies, the representation of satellite field-of-view ellipses, and the emissivity retrieval inside the footprint area are discussed. Furthermore, the simulated brightness temperatures and the sub-footprint variability are analysed in a case study indicating particular areas where the use of the footprint operator is expected to provide significant added value. For radiances measured by the Advanced Microwave Sounding Unit-A (AMSU-A) and Microwave Humidity Sounder (MHS) sensors, the standard deviation of the observation minus background (OmB) departures are computed on a short period in order to compare the statistics of the default and the implemented footprint observation operator. For all operationally used AMSU-A and MHS channels, it is shown that the standard deviation of OmB departures is reduced when the footprint operator is applied. [ABSTRACT FROM AUTHOR]

In this paper, the transformed sine Dagum distribution is proposed using the Dagum distribution as a baseline distribution in the transformed sin-G family of distributions. The purpose of this paper is to propose and explore a modified version of the Dagum distribution, based on the transformed sin-G family of distributions. The density of the transformed sine Dagum distribution shows that it can adequately model datasets that are positively skewed, approximately symmetric and decreasing. The hazard rate plot shows that the proposed distribution can adequately model both monotonic and non-monotonic hazard rate datasets. Statistical properties such quantile function, moments, inverse moments, moments generating functions, mean and median deviation and order statistics are derived. The plots of the skewness and kurtosis show that the skewness is always positive and the kurtosis is increasing. Maximum likelihood estimation is used to estimate the parameters of the transformed sine Dagum distribution. Monte Carlo simulations are performed to ascertain the behavior of the estimators. The results show that the estimators are consistent. The proposed distribution is applied to two real life datasets. The results show that the proposed distribution provide a reasonable parametric fit to the datasets compared with the other competing distribution. [ABSTRACT FROM AUTHOR]

The representability of the Burr distribution as a mixture of Weibull distribution is studied in order to justify its utility for modelling the statistical regularities in extreme values registered in non-stationary flows of informative events. A result of [24] is improved by extending the domain of admissible values of the parameters which provide the representability of the (generalized) Burr distribution as a scale mixture of the Weibull distribution. This result gives an argument in favour of application of the Burr distribution as a model of statistical regularities of extreme values registered within moderate regular time intervals, say, daily (short-term) extremes. In turn, if we are interested in the statistical regularities of the behaviour of the absolute extreme observation over a long period, say, a decade (the long-term extreme), then it can be noted that the daily extreme values form a sample of the Burr-distributed random variables. As is known, the Burr distribution belongs to the domain of max-attraction of the Fréchet distribution. The problem of improving the accuracy of the approximation of the distribution of the absolute extreme by the Fréchet distribution by the construction of an asymptotic expansion for the distribution of the extreme order statistics in the sample of independent identically Burr-distributed random variables is also considered. These results are illustrated by an example of fitting the Burr distribution to the data representing the extreme values of characteristics of the interplanetary magnetic field. [ABSTRACT FROM AUTHOR]

The effective use of available information in extreme value analysis is critical because extreme values are scarce. Thus, using the r largest order statistics (rLOS) instead of the block maxima is encouraged. Based on the four-parameter kappa model for the rLOS (rK4D), we introduce a new distribution for the rLOS as a special case of the rK4D. That is the generalized logistic model for rLOS (rGLO). This distribution can be useful when the generalized extreme value model for rLOS is no longer efficient to capture the variability of extreme values. Moreover, the rGLO enriches a pool of candidate distributions to determine the best model to yield accurate and robust quantile estimates. We derive a joint probability density function, the marginal and conditional distribution functions of new model. The maximum likelihood estimation, delta method, profile likelihood, order selection by the entropy difference test, cross-validated likelihood criteria, and model averaging were considered for inferences. The usefulness and practical effectiveness of the rGLO are illustrated by the Monte Carlo simulation and an application to extreme streamflow data in Bevern Stream, UK. [ABSTRACT FROM AUTHOR]

In reliability theory, the kth order statistic represents the lifetime of a (n - k + 1) -out-of-n system. In particular, the smallest (largest) order statistics denotes the lifetime of a series (parallel) system that consist of n components; and the second smallest (second largest) order statistics is the lifetime of a (n - 1) -out-of-n (2-out-of-n) system. In this paper, sufficient conditions are provided to compare the smallest and the second smallest (largest and second largest) order statistics of dependent and heterogeneous random variables having the additive hazard model with the Archimedean copula in the sense of usual stochastic order and hazard rate order. Further, we compare the smallest order statistics of two sets of independent and heterogeneous random variables having the additive hazard model in the sense of dispersive order. Finally, our theoretical findings are evaluated by some numerical examples and counterexamples. [ABSTRACT FROM AUTHOR]

In this article, we consider stochastic comparisons between second-order statistics arising from general exponentiated location-scale models. When the random variables are independent, we establish usual stochastic and hazard rate orders between second-order statistics. Further, similar ordering results are obtained when the random observations are dependent. Some applications of the established results are presented. [ABSTRACT FROM AUTHOR]

We propose a general framework to construct self-normalized multiple-change-point tests with time series data. The only building block is a user-specified single-change-detecting statistic, which covers a large class of popular methods, including the cumulative sum process, outlier-robust rank statistics, and order statistics. The proposed test statistic does not require robust and consistent estimation of nuisance parameters, selection of bandwidth parameters, nor pre-specification of the number of change points. The finite-sample performance shows that the proposed test is size-accurate, robust against misspecification of the alternative hypothesis, and more powerful than existing methods. Case studies of the Shanghai-Hong Kong Stock Connect turnover are provided. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the problem of stochastically comparing the second-order statistics from dependent and heterogeneous samples following modified proportional hazard rates scale (MPHRS) and modified proportional reversed hazard rates scale (MPRHRS) models under Archimedean copula. We built some sufficient conditions for the usual stochastic order whenever the samples have different parameter vectors. Finally, some numerical examples were provided to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

This work utilizes generalized order statistics (GOSs) to study the q-Weibull distribution from several statistical perspectives. First, we explain how to obtain the maximum likelihood estimates (MLEs) and utilize Bayesian techniques to estimate the parameters of the model. The Fisher information matrix (FIM) required for asymptotic confidence intervals (CIs) is generated by obtaining explicit expressions. A Monte Carlo simulation study is conducted to compare the performances of these estimates based on type II censored samples. Two well-established measures of information are presented, namely extropy and weighted extropy. In this context, the order statistics (OSs) and sequential OSs (SOSs) for these two measures are studied based on this distribution. A bivariate q-Weibull distribution based on the Farlie-Gumbel-Morgenstern (FGM) family and its relevant concomitants are studied. Finally, two concrete instances of medical real data are ultimately provided. [ABSTRACT FROM AUTHOR]

AbstractIn this article, the extreme-value distribution of the partial maximum for a random sequence of the normal-skew-normal (NSN) distribution, to the Gumbel distribution, is derived. The asymptotic distribution of the normalized maximum and its optimal convergence rate are determined using the optimal choice of normalizing constants. These results are applied to derive the extreme-value distributions of minimum and maximum for the exchangeable trivariate normal random vectors, and lifetimes of parallel and series systems having three dependent log-normal components. [ABSTRACT FROM AUTHOR]

In this manuscript, a new probability model named as Sine Power Rayleigh distribution (SPRD) is proposed using a Sine-G function as generator. Various statistical properties of this new distribution were investigated, including the survival function, hazard function, reverse hazard rate, cumulative hazard function, mills ratio, quantile function, moments, moment generating function, conditional moments, entropy, and order statistics. The parameters of the proposed distribution were estimated using the method of maximum likelihood estimation. To assess the model's versatility and applicability, we conduct analyses on two real life data sets. The outcomes affirm the superior performance of the newly proposed model SPRD as compared to existing models. [ABSTRACT FROM AUTHOR]

As the dimensions of available data for analysis continues to grow rapidly, it becomes imperative to develop new probability distributions that can more accurately represent various phenomena. In this research paper, we introduce a novel continuous probability distribution known as the Type II Half-Logistic Exponentiated Frechet Distribution, characterized by four positive parameters. This distribution expands upon the traditional Frechet distribution by introducing two additional parameters. We derive a significant density representation for this distribution. Furthermore, we delve into several statistical and mathematical properties associated with the Type II Half-Logistic Exponentiated Frechet distribution. This includes explicit expressions for key metrics such as the quantile function, probability weighted moments, moments, moments generating function, reliability function, hazard function, and order statistics. To estimate the model parameters effectively, we employ a maximum likelihood estimation technique and present the results of a simulation study. Our research underscores the superiority of this new distribution by applying it to two real-world datasets. Notably, the findings demonstrate that the Type II Half-Logistic Exponentiated Frechet distribution outperforms other considered distributions in fitting the two real datasets. [ABSTRACT FROM AUTHOR]

Based on published and new data for explosive events at Stromboli (Italy), we propose an empirical relation that links mass discharge rate (MDR) and at-vent gas jet velocity (Gv). We use 65 simultaneous measurements of MDR and Gv and find two trends in both the cross-correlation and rank order statistics. Cross-correlation gives a power law relation: M D R = 10 (0.015 G v + 2.434) kg/s, R2 = 0.81, and applies to ash-dominated emissions. Combining this relation with the conservation of mass equation allows at-vent plume density and/or vent area to be derived from MDR = GvρA, ρ being plume density and A being vent cross-sectional area. We find that while a vent radius of 2 m and plume density of 0.35 kg/m3 fits with the "normal" activity at Stromboli, a 290 × 2.5 m vent area likely feeds a 10 kg/m3 jet during paroxysmal activity. Initial tests on available data shows promise in extending the correlation beyond Stromboli and/or to events with higher MDR (> 107 kg/s). However, the exact relation will depend on magma composition, temperature and volatile content, as well as conduit radius and vent overpressure. [ABSTRACT FROM AUTHOR]

BACKGROUND: Recurrent acute pancreatitis is a common acute abdominal disease in surgery. OBJECTIVE: To evaluate the radiographic features of pancreatic computed tomography (CT) imaging in the diagnosis of acute and chronic pancreatitis. METHODS: 48 pancreatitis patients who met the criteria were selected in this retrospective study from 2010 to 2019. Each diagnosis was evaluated as functional abdominal pain, recurrent acute pancreatitis, or chronic pancreatitis. All clinical data were collected from the patient's medical records. 54 radiological features were extracted from each region of interest in outline the pancreas and divided into five categories: first order statistics, the gray level co-occurrence matrix (GLCM), the gray level run-length matrix (GLRLM), the neighborhood gray level difference matrix (NGTDM), and morphological features by the MATLAB program. RESULTS: Of the 48 patients, 16 had functional abdominal pain (33.3%), 18 had recurrent acute pancreatitis (37.5%), and 14 had chronic pancreatitis (29.2%). In the univariate analysis, nine radiological features, eight GLCM features and one NGTDM feature were significantly different between groups. Nine radiological characteristics had important reference values with AUC values ranging from 0.73–0.91. CONCLUSION: Nine radiographic features of CT imaging demonstrate good evaluation efficiency in the diagnosis of pancreatitis and can distinguish patients with functional abdominal pain, recurrent acute pancreatitis, and chronic pancreatitis. [ABSTRACT FROM AUTHOR]

With the growing scarcity of spectrum resources, wideband spectrum sensing is necessary to process a large volume of data at a high sampling rate. For some applications, only second-order statistics are required for spectrum estimation. In this case, a fast power spectrum sensing solution is proposed based on the generalized coprime sampling. The solution involves the inherent structure of the sensing vector to reconstruct the autocorrelation sequence of inputs from sub-Nyquist samples, which requires only parallel Fourier transform and simple multiplication operations. Thus, it takes less time than the state-of-the-art methods while maintaining the same performance, and it achieves higher performance than the existing methods within the same execution time without the need to pre-estimate the number of inputs. Furthermore, the influence of the model mismatch has only a minor impact on the estimation performance, allowing for more efficient use of the spectrum resource in a distributed swarm scenario. Simulation results demonstrate the low complexity in sampling and computation, thus making it a more practical solution for real-time and distributed wideband spectrum sensing applications. [ABSTRACT FROM AUTHOR]

Learning the latent network structure from large scale multivariate point process data is an important task in a wide range of scientific and business applications. For instance, we might wish to estimate the neuronal functional connectivity network based on spiking times recorded from a collection of neurons. To characterize the complex processes underlying the observed data, we propose a new and flexible class of nonstationary Hawkes processes that allow both excitatory and inhibitory effects. We estimate the latent network structure using an efficient sparse least squares estimation approach. Using a thinning representation, we establish concentration inequalities for the first and second order statistics of the proposed Hawkes process. Such theoretical results enable us to establish the non-asymptotic error bound and the selection consistency of the estimated parameters. Furthermore, we describe a least squares loss based statistic for testing if the background intensity is constant in time. We demonstrate the efficacy of our proposed method through simulation studies and an application to a neuron spike train dataset. for this article are available online. [ABSTRACT FROM AUTHOR]

Traditional quantile estimators that are based on one or two order statistics are a common way to estimate distribution quantiles based on the given samples. These estimators are robust, but their statistical efficiency is not always good enough. A more efficient alternative is the Harrell-Davis quantile estimator which uses a weighted sum of all order statistics. Whereas this approach provides more accurate estimations for the light-tailed distributions, it's not robust. To be able to customize the tradeoff between statistical efficiency and robustness, we could consider a trimmed modification of the Harrell-Davis quantile estimator. In this approach, we discard order statistics with low weights according to the highest density interval of the beta distribution. [ABSTRACT FROM AUTHOR]

People's perceptions of Autonomous Vehicles (AVs) are critical to understanding the role of AVs in future transportation systems. Most previous work on AVs perceptions is based on large cities or metropolitan areas. This study provides a unique perspective regarding perceptions of impacts of AVs in small and rural communities through an online survey in Central Texas (n = 1153). Our questionnaires gathered basic socio-demographic characteristics and AV impacts variables identified from the literature. We used summary statistics and ordered logistic regression models to reveal the perceived impacts of AVs. Residents of small and rural communities, particularly older adults (65 + years), were more enthusiastic about the development of AVs than the national average. Our findings reveal that being an employed, married male with a higher income increases the likelihood of accepting the impacts of AVs, suggesting further research to explore a feasible approach to utilizing AVs in small, rural communities. [ABSTRACT FROM AUTHOR]

Let (Ω , Σ , p) be a probability measure space and let X : Ω → R k be a (vector valued) random variable. We suppose that the probability pX induced by X is absolutely continuous with respect to the Lebesgue measure on R k and set fX as its density function. Let ϕ : R k → R n be a C1-map and let us consider the new random variable Y = ϕ (X) : Ω → R n. Setting m : = max { rank (J ϕ (x)) : x ∈ R k } , we prove that the probability pY induced by Y has a density function fY with respect to the Hausdorff measure H m on ϕ (R k) which satisfies f Y (y) = ∫ ϕ − 1 (y) f X (x) 1 J m ϕ (x) d H k − m (x) , for H m − a. e. y ∈ ϕ (R k). Here J m ϕ is the m-dimensional Jacobian of ϕ. When J ϕ has maximum rank we allow the map ϕ to be only locally Lipschitz. We also consider the case of X having probability concentrated on some m-dimensional sub-manifold E ⊆ R k and provide, besides, several examples including algebra of random variables, order statistics, degenerate normal distributions, Chi-squared and "Student's t" distributions. [ABSTRACT FROM AUTHOR]

In this paper, we discuss some theoretical results and properties of a discrete version of the Birnbaum-Saunders distribution. We present a proof of the unimodality of this model. Moreover, results on moments, quantile function, reliability and order statistics are also presented. In addition, we propose a regression model based on the discrete Birnbaum-Saunders distribution. The model parameters are estimated by the maximum likelihood method and a Monte Carlo study is performed to evaluate the performance of the estimators. Finally, we illustrate the proposed methodology with the use of real data sets. [ABSTRACT FROM AUTHOR]

A problem with the estimation of quantiles occurs when the sample comes from an unknown distribution. The estimation uses the bootstrap method in the version that the literature refers to as exact. Three bootstrap estimators were used: two of them based on one order statistic, and the third on a linear combination of two order statistics (for an integer). The distribution of the exact bootstrap estimator based on a single order statistic is known. It has been shown that there is no general form of the distribution of the exact bootstrap estimator based on two order statistics. However, it is possible to calculate such a distribution - the article presents the algorithm that performs such a task. The bootstrap confidence intervals were constructed using the exact percentile method. It has been shown that if the estimator is based on a single order statistic, it is known in advance which elements of the primary sample are the limits of the confidence intervals, so there is no need to resample. The intervals determined by the exact percentile method were compared with those constructed using other methods. It has been shown that the information on the direction of the asymmetry of the distribution that the sample comes from is worth considering when selecting the rank of the order statistic used as an estimator. Attention is paid to the influence of the quality of the pseudorandom number generators on the results of the Monte Carlo simulation. [ABSTRACT FROM AUTHOR]

The Social Package for the Social Sciences (SPSS) is among the most common programs used by researchers in language studies to explore, examine, and analyze quantitative data for the sake of drawing valid conclusions. The current action research aims to offer insights into the utilization of SPSS by Master's students in their empirical studies for statistical analysis. Specifically, it attempts to depict the way SPSS is employed in academic pursuits, and discern the inherent challenges faced by students, offering insights into the obstacles that may impede their effective use of SPSS as a tool for statistical exploration and interpretation in academic research. To reach these objectives, ten Master’s dissertations written by EFL students at the Department of English at Mouloud Mammeri University in language studies were scrutinized though a qualitative content analysis. Findings indicate that the students limit the scope of their use of SPSS to quantitative variables and descriptive statistics. In addition, it has been found that the most commonly used statistical technique is ‘the mean’ or ‘the average’ that could be easily measured without any sophisticated software. Furthermore, no reference to inferential statistics in order to compare among groups or to measure the impact of a variable on another is made. The overall conclusion drawn from the analysis of the corpus is that students exhibit reluctance to the use of inferential statistics in their empirical studies and unconsciously believe that SPSS, inferential statistics, or any other sophisticated software are tightly related to natural sciences and could not be easily applied in social sciences. On the basis of the findings, a number of recommendations are suggested like organizing workshops with computer scientists. In addition, students’ self-confidence should be increased in order to change their perception of their potential and abilities to feel more at ease with statistics and technologies while doing academic research in language studies. [ABSTRACT FROM AUTHOR]

Recently, extropy has emerged as an alternative measure of uncertainty instead of entropy. When it comes to quantifying uncertainty regarding the remaining lifetime of a component, entropy has proven to be less effective. Therefore, the concept of residual entropy was introduced to address this limitation. Similar to the residual entropy, the residual extropy was formulated and used to investigate the uncertainty in the residual lifetime of a unit. Systems in the real world exhibit a pervasive property of uncertainty that affects future events and past events. For this reason, the concept of past extropy was introduced to specifically capture and analyze the uncertainty associated with past events. This paper focuses on stochastic aspects, including stochastic orderings, which provide useful inequalities related to past extropy when applied to order statistics and lower record values. It is worth noting that the past extropy of the i th-order statistics and record values in the continuous case is related to the past extropy of the i th-order statistics and record values evaluated from the uniform distribution. The monotonicity of the past extropy of order statistics is examined and some insights into the past extropy of lower data set values are also given. Finally, some computational results are presented. In fact, an estimator for the extropy of the exponential distribution is proposed. For this purpose, the maximum likelihood estimator is derived. The proposed method is easy to implement and apply from a computational point of view. [ABSTRACT FROM AUTHOR]

Today's teenagers are dealing with anxiety and stress. Anxiety, depression, and suicide rates have increased in recent years because of increased social rivalry. The research is focused on detecting anxiety in students due to exam pressure to reduce the potential harm to a person's wellness. Research is performed on databases for anxious states based on psychological stimulation (DASPS) and our own database. The measured signal is divided into sub bands that correspond to the electroencephalogram (EEG) rhythms using the Butterworth sixth-order order filter. In higher dimensional space, the nonlinearities of each sub-band signal are analyzed using higher order statistics third-order cumulants (TOC). We have classified stress and anxiety using the support vector machine (SVM), K-nearest neighbor (K-NN), and deep learning bidirectional long short-term memory (BiLSTM) network. In comparison to previous techniques, the proposed system's performance using BiLSTM is quite good. The best accuracy in this analysis was 87% on the DASPS database and 98% on the own database. Finally, subjects with high stress levels had more gamma activity than subjects with little stress. This could be an important attribute in the classification of stress. [ABSTRACT FROM AUTHOR]

We introduced a flexible class of continuous distributions called the generalized Kavya-Manoharan-G (GKM-G) family. The GKM-G family extended the Kavya-Manoharan class and provided greater flexibility to the baseline models. The special sub-models of the GKM-G family are capable of modeling monotone and non-monotone failure rates including increasing, reversed J shape, decreasing, bathtub, modified bathtub, and upside-down bathtub. Some properties of the family were studied. The GKM-exponential (GKME) distribution was studied in detail. Eight methods of estimation were used for estimating the GKME parameters. The performance of the estimators was assessed by simulation studies under small and large samples. Furthermore, the flexibility of the two-parameter GKME distribution was explored by analyzing five real-life data applications from applied fields such as medicine, environment, and reliability. The data analysis showed that the GKME distribution outperforms other competing exponential models.

BackgroundThe growing amount of high dimensional biomolecular data has spawned new statistical and computational models for risk prediction and disease classification. Yet, many of these methods do not yield biologically interpretable models, despite offering high classification accuracy. An exception, the top-scoring pair (TSP) algorithm derives parameter-free, biologically interpretable single pair decision rules that are accurate and robust in disease classification. However, standard TSP methods do not accommodate covariates that could heavily influence feature selection for the top-scoring pair. Herein, we propose a covariate-adjusted TSP method, which uses residuals from a regression of features on the covariates for identifying top scoring pairs. We conduct simulations and a data application to investigate our method, and compare it to existing classifiers, LASSO and random forests.ResultsOur simulations found that features that were highly correlated with clinical variables had high likelihood of being selected as top scoring pairs in the standard TSP setting. However, through residualization, our covariate-adjusted TSP was able to identify new top scoring pairs, that were largely uncorrelated with clinical variables. In the data application, using patients with diabetes (n = 977) selected for metabolomic profiling in the Chronic Renal Insufficiency Cohort (CRIC) study, the standard TSP algorithm identified (valine-betaine, dimethyl-arg) as the top-scoring metabolite pair for classifying diabetic kidney disease (DKD) severity, whereas the covariate-adjusted TSP method identified the pair (pipazethate, octaethylene glycol) as top-scoring. Valine-betaine and dimethyl-arg had, respectively, ≥ 0.4 absolute correlation with urine albumin and serum creatinine, known prognosticators of DKD. Thus without covariate-adjustment the top-scoring pair largely reflected known markers of disease severity, whereas covariate-adjusted TSP uncovered features liberated from confounding, and identified independent prognostic markers of DKD severity. Furthermore, TSP-based methods achieved competitive classification accuracy in DKD to LASSO and random forests, while providing more parsimonious models.ConclusionsWe extended TSP-based methods to account for covariates, via a simple, easy to implement residualizing process. Our covariate-adjusted TSP method identified metabolite features, uncorrelated from clinical covariates, that discriminate DKD severity stage based on the relative ordering between two features, and thus provide insights into future studies on the order reversals in early vs advanced disease states.

In this article, we discuss sufficient conditions for the hazard rate order on smallest order statistics for variables with Archimedean survival copula and having modified proportional hazard rates (modified scale) model. We also establish the reversed hazard rate order on largest order statistics from variables with Archimedean copula and having modified proportional reversed hazard rates model. The results established here extend the recent results of Li and Li (2019). [ABSTRACT FROM AUTHOR]

Many researchers have proposed numerous Bayesian predictive densities for Type-II censored data that is generated by ordered observations. However, their evaluations of predictive densities were insufficient because the Bayesian predictive density includes prior parameters, thus we suffer from the selection of the prior parameters. In this study, we consider two types of predictive densities, posterior predictive and plug-in, for observations from an exponential distribution of Type-II censored data. We discuss a suitable predictive density using the risk with the Kullback–Leibler loss function. In our setting, we consider a Gamma prior, which is a conjugate prior for mathematical tractability. We prove that the posterior predictive density with an improper Gamma prior provides the dominance of the posterior predictive density over the plug-in densities without depending on the selection of an unknown parameter in our setting. Finally, we show that the posterior predictive density outperforms the plug-in densities in terms of coverage probabilities for unobserved data by censoring in a simulation study. [ABSTRACT FROM AUTHOR]

In many industries, the reliability of a product is often determined by a quantile of a distribution of a product's characteristics meeting a specified requirement. A typical approach to address this is to assume a parametric model and compute a one‐sided confidence bound on the quantile. However, this can become difficult if the sample size is too small to reliably estimate such a parametric model. Linear interpolation between order statistics is a viable nonparametric alternative if the sample size is sufficiently large. In most cases, linear extrapolation from the extreme order statistics can be used, but can result in inconsistent coverage. In this work, we perform an empirical study to generate robust weights for linear extrapolation that greatly improves the accuracy of the coverage across a feasible range of distribution families with positive support. Our method is applied to two industrial datasets. [ABSTRACT FROM AUTHOR]

The convergence of a sequence of point processes with dependent points, defined by a symmetric function of iid high-dimensional random vectors, to a Poisson random measure is proved. This also implies the convergence of the joint distribution of a fixed number of upper order statistics. As applications of the result a generalization of maximum convergence to point process convergence is given for simple linear rank statistics, rank-type U-statistics and the entries of sample covariance matrices. [ABSTRACT FROM AUTHOR]

We study the weak convergence of the extremes of supercritical branching Lévy processes $\{\mathbb{X}_t, t \ge0\}$ whose spatial motions are Lévy processes with regularly varying tails. The result is drastically different from the case of branching Brownian motions. We prove that, when properly renormalized, $\mathbb{X}_t$ converges weakly. As a consequence, we obtain a limit theorem for the order statistics of $\mathbb{X}_t$. [ABSTRACT FROM AUTHOR]

More than half a century ago, it was proved that the increasing failure rate (IFR) property is preserved under the formation of k -out-of- n systems (order statistics) when the lifetimes of the components are independent and have a common absolutely continuous distribution function. However, this property has not yet been proved in the discrete case. Here we give a proof based on the log-concavity property of the function $f({{\mathrm{e}}}^x)$. Furthermore, we extend this property to general distribution functions and general coherent systems under some conditions. [ABSTRACT FROM AUTHOR]

Preservation of stochastic orders through the system signature has captured the attention of researchers in recent years. Signature-based comparisons have been made for the usual stochastic order, hazard rate order, and likelihood ratio orders. However, for the mean residual life (MRL) order, it has recently been proved that the preservation result does not hold true in general, but rather holds for a particular class of distributions. In this paper, we study whether or not a similar preservation result holds for the mean inactivity time (MIT) order. We prove that the MIT order is not preserved from signatures to system lifetimes with independent and identically distributed (i.i.d.) components, but holds for special classes of distributions. The relationship between these classes and the order statistics is also highlighted. Furthermore, the distribution-free comparison of the performance of coherent systems with dependent and identically distributed (d.i.d.) components is studied under the MIT ordering, using diagonal-dependent copulas and distorted distributions. [ABSTRACT FROM AUTHOR]

Developed sequential order statistics (DSOS) are very useful in modeling the lifetimes of systems with dependent components, where the failure of one component affects the performance of remaining surviving components. We study some stochastic comparison results for DSOS in both one-sample and two-sample scenarios. Furthermore, we study various ageing properties of DSOS. We state many useful results for generalized order statistics as well as ordinary order statistics with dependent random variables. At the end, some numerical examples are given to illustrate the proposed results. [ABSTRACT FROM AUTHOR]

This article aims to discuss different estimation methods for the power generalized Weibull distribution. An extensive simulation study is carried out to assess the effectiveness of the estimation of model parameters using numerous well known classical methods of estimation. Furthermore, the Bayes estimators of the unknown parameters are also obtained under different loss functions. Monte Carlo simulations are used to assess the performances of the proposed estimators. Besides, bootstrap/ credible intervals are obtained based on considered methods of estimation. Finally, the potentiality of the distribution is illustrated by means of re-analyzing one real data set.

Recently, extropy has emerged as an alternative measure of uncertainty instead of entropy. When it comes to quantifying uncertainty regarding the remaining lifetime of a component, entropy has proven to be less effective. Therefore, the concept of residual entropy was introduced to address this limitation. Similar to the residual entropy, the residual extropy was formulated and used to investigate the uncertainty in the residual lifetime of a unit. Systems in the real world exhibit a pervasive property of uncertainty that affects future events and past events. For this reason, the concept of past extropy was introduced to specifically capture and analyze the uncertainty associated with past events. This paper focuses on stochastic aspects, including stochastic orderings, which provide useful inequalities related to past extropy when applied to order statistics and lower record values. It is worth noting that the past extropy of the $ i $th-order statistics and record values in the continuous case is related to the past extropy of the $ i $th-order statistics and record values evaluated from the uniform distribution. The monotonicity of the past extropy of order statistics is examined and some insights into the past extropy of lower data set values are also given. Finally, some computational results are presented. In fact, an estimator for the extropy of the exponential distribution is proposed. For this purpose, the maximum likelihood estimator is derived. The proposed method is easy to implement and apply from a computational point of view.

We evaluate, in the large- N limit, the complete probability distribution P (A , m) of the values A of the sum ∑ i = 1 N | λ i | m , where λ i ( i = 1 , 2 , ... , N ) are the eigenvalues of a Gaussian random matrix, and m is a positive real number. Combining the Coulomb gas method with numerical simulations using a matrix variant of the Wang–Landau algorithm, we found that, in the limit of N → ∞ , the rate function of P (A , m) exhibits phase transitions of different characters. The phase diagram of the system on the (A, m) plane is surprisingly rich, as it includes three regions: (i) a region with a single-interval support of the optimal spectrum of eigenvalues, (ii) a region emerging for m < 2 where the optimal spectrum splits into two separate intervals, and (iii) a region emerging for m > 2 where the maximum or minimum eigenvalue 'evaporates' from the rest of eigenvalues and dominates the statistics of A. The phase transition between regions (i) and (iii) is of second order. Analytical arguments and numerical simulations strongly suggest that the phase transition between regions (i) and (ii) is of (in general) fractional order p = 1 + 1 / | m − 1 | , where 0 < m < 2 . The transition becomes of infinite order in the special case of m = 1, where we provide a more complete analytical and numerical description. Remarkably, the transition between regions (i) and (ii) for m ⩽ 1 and the transition between regions (i) and (iii) for m > 2 occur at the ground state of the Coulomb gas which corresponds to the Wigner's semicircular distribution. [ABSTRACT FROM AUTHOR]

Background: The Modified Framingham Stroke Risk Score (MFSRS) is a widely utilized stroke risk assessment algorithm usually applied in international comparison. The Stroke Investigative Research and Educational Network (SIREN) is the only known African-specific stroke risk assessment algorithm. Aims and objectives: To compare stroke risk estimates from the SIREN and the MFSRS in an African community. Methods: This was a population-based cross-sectional survey involving consecutively recruited 310 consenting adult residents (mean age = 37.21 ± 15.84 years) of a Nigerian community. Risk factors of stroke were assessed among the participants and were utilized in calculating stroke risk estimates on the MFSRS and the SIREN. The obtained data were analyzed using descriptive statistics and the Spearman-rank order correlation test at an alpha level of 0.05. Results: The percentage stroke risk scores estimated by the SIREN and the MFSRS were 34.5% and 6.79% respectively. The most prevalent risk factors among the participants were hypertriglyceridemia (100.0%), raised waist-hip ratio (50.6%), hypercholesterolemia (45.5), physical inactivity (43.2%), psychological stress (41.3%), and hypertension (37.7%). Only two (hypertriglyceridemia and high blood pressure) out of the six factors considered in the MFSRS were rated among the first 10 most impactful risks by the SIREN. There was a weak correlation between the total scores on the MFSRS and the SIREN (rho = 0.39; p < 0.01) suggesting that the two ratings were discordant. Conclusion: There were disagreements between the risk estimates on the SIREN and MFSRS with SIREN having a higher estimate that corresponded with the literature; this may be suggesting a poorer estimation of stroke risks by the MFSRS in an African environment. There is a need for large African-based quality control studies to determine and address these lapses. [ABSTRACT FROM AUTHOR]

The problem of examining how well the data fit a supposed distribution is very important, and it must be confirmed prior to any data analysis, because many data analysis methods assume a specific distribution of data. For this purpose, histograms or Q-Q plots are employed for the assessment of data distribution. Additionally, a GoF TstS utilizes distance measurements between the empirical distribution function and the theoretical cumulative distribution function (cdf) to evaluate data distribution. In life-testing or reliability studies, the observed failure time of test units may not be recorded in some situations. The GoF TstSs for completely observed data can no longer be used in progressive type II censored data (PrCsD). In this paper, we suggest a GoF TstSs and new plot method for the GoF test of symmetric and asymmetric location-scale distribution (LoScD) based on PrCsD. The power of the suggested TstSs is estimated through Monte Carlo (MC) simulations, and it is compared with that of the TstSs using the order statistics (OrSt). Furthermore, we analyzed real data examples (symmetric and asymmetric data). [ABSTRACT FROM AUTHOR]

In parametric statistical modeling, it is essential to create generalizations of current statistical distributions that are more flexible when modeling actual data sets. Therefore, this study introduces a new generalized lifetime model named the odd Weibull Inverse Gompertz distribution (OWIG). The OWIG is derived by combining the odd Weibull family of distributions with the inverse Gompertz distribution. Essential statistical properties are discussed, including reliability functions, moments, Rényi entropy, and order statistics. The proposed OWIG is particularly significant as its hazard rate functions exhibit various monotonic and nonmonotonic shapes. This enables OWIG to model different hazard behaviors more commonly observed in natural phenomena. OWIG's parameters are estimated and its flexibility in predicting unique symmetric and asymmetric patterns is shown by analyzing real-world applications from psychology, environmental, and medical sciences. The results demonstrate that the proposed OWIG is an excellent candidate as it provides the most accurate fits to the data compared with some competing models. [ABSTRACT FROM AUTHOR]

We show that the expected value of the largest order statistic in Gaussian samples can be accurately approximated as (0.2069 ln (ln (n)) + 0.942) 4 , where n ∈ [ 2 , 10 8 ] is the sample size, while the standard deviation of the largest order statistic can be approximated as − 0.4205 arctan (0.5556 [ ln (ln (n)) − 0.9148 ]) + 0.5675. We also provide an approximation of the probability density function of the largest order statistic which in turn can be used to approximate its higher order moments. The proposed approximations are computationally efficient, and improve previous approximations of the mean and standard deviation given by Chen and Tyler (1999). [ABSTRACT FROM AUTHOR]