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This paper examines the Wasserstein metric between the empirical probability measure of n discrete random variables and a continuous uniform measure in the d-dimensional ball, providing an asymptotic estimation of their expectations as n approaches infinity. Furthermore, we investigate this problem within a mixed process framework, where n discrete random variables are generated by the Poisson process. [ABSTRACT FROM AUTHOR]

Comfort has traditionally been assessed as a single deterministic index that can be assigned to each railway vehicle type (at a given speed on a given track quality level). However, it is now well established that passengers influence vibration and, as a consequence, occupancy level and seating arrangement influence comfort, thus turning it into a stochastic variable. The concept of Compound Comfort, presented in Palomares et al. [Is the standard ride comfort index an actual estimation of railway passenger comfort? Veh Syst Dyn. 2022;1–14. doi: ], is used in this paper to evaluate several train types. Simplified models are used as a first approximation for vibration analysis. Despite model simplicity, since the number of possible seating arrangements is intractable, a Monte Carlo procedure is used to obtain compound comfort probability density distributions from a randomised subset of cases. The results from the work presented here will show that the information provided by stochastic distributions is much richer than a single deterministic index. Nevertheless, obtaining distributions from Monte Carlo tests (numerical or experimental) is impractical for any commercial assessment of comfort. Therefore, an inference procedure is called for and has been devised in order to obtain probability density function parameters from just one tare test, along with ten runs of a half laden test. This recipe has been adapted from one presented previously to be able to accommodate the skewed distributions that emerge when a wide range of train configurations is considered. [ABSTRACT FROM AUTHOR]

Because it is generally impossible to completely characterize the uncertainty in complex model variables after assimilation of data, it is common to approximate the uncertainty by sampling from approximations of the posterior distribution for model variables. When minimization methods are used for the sampling, the weights on each of the samples depend on the magnitude of the data mismatch at the critical points and on the Jacobian of the transformation from the prior density to the sample proposal density. For standard iterative ensemble smoothers, the Jacobian is identical for all samples, and the weights depend only on the data mismatch. In this paper, a hybrid data assimilation method is proposed which makes it possible for each ensemble member to have a distinct Jacobian and for the approximation to the posterior density to be multimodal. For the proposed hybrid iterative ensemble smoother, it is necessary that a part of the mapping from the prior Gaussian random variable to the data be analytic. Examples might include analytic transformation from a latent Gaussian random variable to permeability followed by a black-box transformation from permeability to state variables in porous media flow, or a Gaussian hierarchical model for variables followed by a similar black-box transformation from permeability to state variables. In this paper, the application of weighting to both hybrid and standard iterative ensemble smoothers is investigated using a two-dimensional, two-phase flow problem in porous media with various degrees of nonlinearity. As expected, the weights in a standard iterative ensemble smoother become degenerate for problems with large amounts of data. In the examples, however, the weights for the hybrid iterative ensemble smoother were useful for improving forecast reliability. [ABSTRACT FROM AUTHOR]

This paper generalizes the concept of capacity from the portfolio level to the investment process for systematic equity strategies. Capacity is often understood as the maximum asset under management, above which additional inflows would have too great a negative impact on performance. The concept of capacity is often limited to the study of a given portfolio. However, setting up a capacity management framework must consider what the portfolio might look like in the future. This is obviously complicated for discretionary portfolios but theoretically conceivable for portfolios implementing systematic strategies, if we can simulate all possible scenarios. In our framework, we extend the traditional definition of capacity from a number to a random variable, allowing portfolio managers to integrate it into their risk considerations. We provide examples of how portfolio managers can approach this problem, with full-search or modelling methods. Our framework includes several capacity metrics that can be used jointly or selected to align better with the features of each strategy. [ABSTRACT FROM AUTHOR]

This paper analyzes the co-fluctuation between a scalar response random variable and a curve regressor using quantile regression. We focus on the situation wherein the output variable is observed with random missing. For this incomplete functional data situation, we estimate the quantile regression by combining two principal nonparametric methods: the local linearity approach (LLA) and the kernel nearest neighbor (KNN) algorithm. We study the asymptotic properties of the constructed estimator by establishing, under general assumptions, uniform consistency over the number of neighborhoods. This asymptotic result provides good mathematical support for the selection of the optimal neighborhood. We examine the feasibility of the constructed estimator using artificially generated data. Moreover, we apply the quantile regression technique in food quality by predicting the riboflavin quantity in yogurt using spectrometry data. [ABSTRACT FROM AUTHOR]

Rooted in dynamic systems theory, convergent cross mapping (CCM) has attracted increased attention recently due to its capability in detecting linear and nonlinear causal coupling in both random and deterministic settings. One limitation with CCM is that it uses both past and future values to predict the current value, which is inconsistent with the widely accepted definition of causality, where it is assumed that the future values of one process cannot influence the past of another. To overcome this obstacle, in our previous research, we introduced the concept of causalized convergent cross mapping (cCCM), where future values are no longer used to predict the current value. In this paper, we focus on the implementation of cCCM in causality analysis. More specifically, we demonstrate the effectiveness of cCCM in identifying both linear and nonlinear causal coupling in various settings through a large number of examples, including Gaussian random variables with additive noise, sinusoidal waveforms, autoregressive models, stochastic processes with a dominant spectral component embedded in noise, deterministic chaotic maps, and systems with memory, as well as experimental fMRI data. In particular, we analyze the impact of shadow manifold construction on the performance of cCCM and provide detailed guidelines on how to configure the key parameters of cCCM in different applications. Overall, our analysis indicates that cCCM is a promising and easy-to-implement tool for causality analysis in a wide spectrum of applications. [ABSTRACT FROM AUTHOR]

Cyber-security research on networked multi-sensor systems is crucial due to the vulnerability to various types of cyberattacks. For the development of effective defense measures, attention is required to gain insight into the complex characteristics and behaviors of cyber attacks from the attacker's perspective. This paper aims to tackle the problem of distributed consensus estimation for networked multi-sensor systems subject to hybrid attacks and missing measurements. To account for both random denial of service (DoS) attacks and false data injection (FDI) attacks, a hybrid attack model on the estimator-to-estimator communication channel is presented. The characteristics of missing measurements are defined by random variables that satisfy the Bernoulli distribution. Then a modified consensus-based distributed estimator, integrated with the characteristics of hybrid attacks and missing measurements, is presented. For reducing the computational complexity of the optimal distributed estimation method, a scalable suboptimal distributed consensus estimator is designed. Sufficient conditions are further provided for guaranteeing the stability of the proposed suboptimal distributed estimator. Finally, a simulation experiment on aircraft tracking is executed to validate the effectiveness and feasibility of the proposed algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we investigate an extended version of the elephant random walk model. Unlike the traditional approach where step sizes remain constant, our model introduces a novel feature: step sizes are generated as a sequence of positive independent and identically distributed random variables, and the step of the walker at time n+1 depends only on the steps of the walker between times 1, ..., mn, where (mn)n⩾1 is a sequence of positive integers growing to infinity as n goes to infinity. Our main results deal with the validity of the central limit theorem for this new variation of the standard ERW model introduced by Schutz and Trimper in 2004. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of H∞ performance analysis of 2D discrete singular stochastic system described by Roesser model which is challenging since it involves 2D random variables and the disturbance simultaneously. Sufficient conditions are established for the regularity, causality and stability of the system. The proposed results are expressed in terms of strict linear matrix inequalities. Furthermore, a mean square asymptotic stability with an $ H_{\infty } $ H ∞ disturbance level is developed. Simulation example is provided in order to illustrate the relevance of our approach. [ABSTRACT FROM AUTHOR]

In this paper, we construct a class of Z 4 Z 4 Z 4 -additive cyclic codes generated by 3-tuples of polynomials. We discuss their algebraic structure and show that generator matrices can be constructed for all codes in this class. We study asymptotic properties of this class of codes by using a Bernoulli random variable. Moreover, let 0 < δ < 1 be a real number such that the entropy h 4 ((k + l + t) δ 6) < 1 4 , we show that the relative minimum distance converges to δ and the rate of the random codes converges to 1 k + l + t , where k, l, and t are pairwise co-prime positive odd integers. Finally, we conclude that the Z 4 Z 4 Z 4 -additive cyclic codes are asymptotically good. [ABSTRACT FROM AUTHOR]

This paper considers a repairable system whose periods of operations and repairs alternate during the run time. The residual lifetime of the system and its age, when the system operates at time $t$ t , are proposed, and their properties are investigated. Under the condition that the system is under repair, the remaining time until the end of system repair time and the elapsed time of a repair are studied. Since computing a renewal function is not straightforward, we use phase-type approximation to find the best-fitted distribution of corresponding random variables. We provide some examples and utilize a real data set to demonstrate the results. [ABSTRACT FROM AUTHOR]

In this paper, we obtain the asymptotic form of the joint distribution of maxima and minima of independent observations, when the sample size is a random variable. We also discuss the asymptotic distribution of the range. [ABSTRACT FROM AUTHOR]

In this paper, for a wide class of nonparametric regression models, new local linear kernel estimators are proposed that are uniformly consistent under close-to-minimal and visual conditions on design points. These estimators are universal in the sense that their designs can be either fixed and not necessarily satisfying the traditional regularity conditions, or random, while not necessarily consisting of independent or weakly dependent random variables. With regard to the design elements, only dense filling of the regression function domain with the design points without any specification of their correlation is assumed. This study extends the dense data methodology and main results of the authors' previous work for the case of regression functions of several variables. [ABSTRACT FROM AUTHOR]

For the RRT* algorithm, there are problems such as greater randomness, longer time consumption, more redundant nodes, and inability to perform local obstacle avoidance when encountering unknown obstacles in the path planning process of autonomous vehicles. And the artificial potential field method (APF) applied to autonomous vehicles is prone to problems such as local optimality, unreachable targets, and inapplicability to global scenarios. A fusion algorithm combining the improved RRT* algorithm and the improved artificial potential field method is proposed. First of all, for the RRT* algorithm, the concept of the artificial potential field and probability sampling optimization strategy are introduced, and the adaptive step size is designed according to the road curvature. The path post-processing of the planned global path is carried out to reduce the redundant nodes of the generated path, enhance the purpose of sampling, solve the problem where oscillation may occur when expanding near the target point, reduce the randomness of RRT* node sampling, and improve the efficiency of path generation. Secondly, for the artificial potential field method, by designing obstacle avoidance constraints, adding a road boundary repulsion potential field, and optimizing the repulsion function and safety ellipse, the problem of unreachable targets can be solved, unnecessary steering in the path can be reduced, and the safety of the planned path can be improved. In the face of U-shaped obstacles, virtual gravity points are generated to solve the local minimum problem and improve the passing performance of the obstacles. Finally, the fusion algorithm, which combines the improved RRT* algorithm and the improved artificial potential field method, is designed. The former first plans the global path, extracts the path node as the temporary target point of the latter, guides the vehicle to drive, and avoids local obstacles through the improved artificial potential field method when encountered with unknown obstacles, and then smooths the path planned by the fusion algorithm, making the path satisfy the vehicle kinematic constraints. The simulation results in the different road scenes show that the method proposed in this paper can quickly plan a smooth path that is more stable, more accurate, and suitable for vehicle driving. [ABSTRACT FROM AUTHOR]

This paper presents a flexible family of 2- and 3-parameter distributions whose support is the closed interval [0,1], with explicit density, cumulative density, and quantile functions. These distributions are suited to modeling quantiles, thereby expanding the toolbox of distributions for doubly-bounded random variables. The densities at the boundaries are determined by dispersion and skew parameters, and a third parameter exclusively influences location. The paper also discusses practical issues of parameter estimation and assesses estimation bias, Type I error-rate accuracy, and parameter-estimate collinearity. It also provides three examples of applications to real data using new packages implementing the distributions in R and Stata. [ABSTRACT FROM AUTHOR]

The paper deals with the stochastic analysis of a two identical unit cold standby system model. As soon as a unit fails it is attended first by assistant repairman, who completes its repair to make it as good as new with fixed known probability p. Otherwise, with probability q( =1-p), the unit repaired by assistant repairman goes to expert repairman so as to make it as good as new. Both the repairmen are always available with the system and they work their jobs simultaneously. The failure time and repair time by assistant repairman are correlated random variables having their joint distribution as Bivariate exponential. Various measures of system effectiveness useful to system designers and operation managers are obtained by using regenerative point technique. The MTSF and steady state profit have also been studied through graphs in respect of parameter alpha for three different values of repair rate by expert repairman and two different values of correlation coefficient between failure and repair times and important conclusions are drawn. [ABSTRACT FROM AUTHOR]

In this paper, the distribution function ϕ(u) = P(supn≥1∑ni=1(Xi − κ) < u), and the generating function of ϕ(u + 1) are set up. We assume that u ∈ N ∪ {0}, κ ∈ N, the random walk {∑ni=1 Xi, n ∈ N} involves N ∈ N periodically occurring distributions, and the integer-valued and nonnegative random variables X1, X2,... are independent. This research generalizes two recent works where {κ = 1, N ∈ N} and {κ ∈ N, N = 1} were considered respectively. The provided sequence of sums {∑ni=1(Xi − κ), n ∈ N} generates the socalled multi-seasonal discrete-time risk model with arbitrary natural premium and its known distribution enables to compute the ultimate time ruin probability 1 − ϕ(u) or survival probability ϕ(u). The obtained theoretical statements are verified in several computational examples where the values of the survival probability ϕ(u) and its generating function are provided when {κ = 2, N = 2}, {κ = 3, N = 2}, {κ = 5, N = 10} and Xi adopts the Poisson and some other distributions. The conjecture on the nonsingularity of certain matrices is posed. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to explore two probability distributions originating from the Kies distribution defined on an arbitrary domain. The first one describes the minimum of several Kies random variables whereas the second one is for their maximum – they are named min- and max-Kies, respectively. The properties of the min-Kies distribution are studied in details, and later some duality arguments are used to examine the max variant. Also the saturations in the Hausdorff sense are investigated. Some numerical experiments are provided. [ABSTRACT FROM AUTHOR]

Purpose: A stochastic technique for solving interval non-linear problems using generalized Hukuhara (GH)-difference is proposed. The non-linear programming problem in interval form is transformed into an equivalent non-linear programming problem with real coefficients by associating a Gaussian random variable to the interval and the six-sigma rule. The conceptualized idea eliminates the decision maker's instinctive selection of weight functions and provides an alternative to the order relation method, max-min criteria-based methods and bi-level approaches for representing intervals as real numbers. To demonstrate a coherent understanding, numerical examples have been used. Design/methodology/approach: A stochastic approach has been used to develop a solution technique for solving interval nonlinear programming problems which arise in the modeling of scientific and engineering problems under uncertain environments. Findings: The proposed idea eliminates the decision maker's instinctive selection of weight functions and provides an alternative to the order relation method, max-min criteria-based methods and bi-level approaches for representing intervals as real numbers. This method provides specific results rather than in the interval form, which are more practical and implementable by the decision maker. Originality/value: This is to certify, that the research paper submitted is an outcome of original work. I have duly acknowledged all the sources from which the ideas and extracts have been taken. This article has not been submitted elsewhere for publication. [ABSTRACT FROM AUTHOR]

The facies distribution of a reservoir is one of the biggest concerns for geologists, geophysicists, reservoir modelers, and reservoir engineers due to its high importance in the setting of any reliable decisionmaking/optimization of field development planning. The approach for parameterizing the facies distribution as a random variable comes naturally through using the probability fields. Since the prior probability fields of facies come either from a seismic inversion or from other sources of geologic information, they are not conditioned to the data observed from the cores extracted from the wells. This paper presents a regularized element-free Galerkin (R-EFG) method for conditioning facies probability fields to facies observation. The conditioned probability fields respect all the conditions of the probability theory (i.e. all the values are between 0 and 1, and the sum of all fields is a uniform field of 1). This property achieves by an optimization procedure under equality and inequality constraints with the gradient projection method. The conditioned probability fields are further used as the input in the adaptive pluri-Gaussian simulation (APS) methodology and coupled with the ensemble smoother with multiple data assimilation (ES-MDA) for estimation and uncertainty quantification of the facies distribution. The history-matching of the facies models shows a good estimation and uncertainty quantification of facies distribution, a good data match and prediction capabilities. [ABSTRACT FROM AUTHOR]

This paper proposes an efficient geotechnical reliability analysis framework that integrates the advantages of the first-order reliability method (FORM) and the Karhunen-Loève expansion (KL) to evaluate the reliability of spatially variable soil slopes. The improved Hasofer-Lind-Rackwitz-Fiessler (iHLRF) recursive algorithm is adopted to implement the FORM procedure when coupled with finite element codes for slope stability analysis, and the KL is used to reduce the dimension of random variables representing the soil random fields. To enhance the accuracy of the failure probability estimated by KL-iHLRF, the importance sampling (IS) is also conducted in this study, resulting in an innovative slope reliability analysis framework, KL-iHLRF-IS. It is found that although the FORM analysis by itself may not be able to confidently estimate the failure probability of spatially variable soil slopes because of the very high dimension of random variables and the strong nonlinearity of the limit state function, it provides useful information on the design point values for KL-iHLRF-IS to rapidly compute the failure probability. The efficiency of KL-iHLRF-IS for slope reliability analysis is illustrated by three example slope case studies. The proposed framework is particularly useful when fast yet accurate slope reliability analysis using the finite element method is needed. [ABSTRACT FROM AUTHOR]

Expected utility theory is critical for modeling rational decision making under uncertainty, guiding economic agents as they seek to optimize outcomes. Traditional methods often require restrictive assumptions about underlying stochastic processes, limiting their applicability. This paper expands the theoretical framework by considering investment returns modeled by a stochastically ordered family of random variables under the convolution order, including Poisson, Gamma, and exponential distributions. Utilizing fractional calculus, we derive explicit, closed-form expressions for the derivatives of expected utility for various utility functions, significantly broadening the potential for analytical and computational applications. We apply these theoretical advancements to a case study involving the optimal production strategies of competitive firms, demonstrating the practical implications of our findings in economic decision making. [ABSTRACT FROM AUTHOR]

This study presents a dynamic Bayesian game model designed to improve predictions of ecological uncertainties leading to natural disasters. It incorporates historical signal data on ecological indicators. Participants, acting as decision-makers, receive signals about an unknown parameter-observations of a random variable's realization values before a specific time, offering insights into ecological uncertainties. The essence of the model lies in its dynamic Bayesian updating, where beliefs about unknown parameters are refined with each new signal, enhancing predictive accuracy. The main focus of our paper is to theoretically validate this approach, by presenting a number of theorems that prove its precision and efficiency in improving uncertainty estimations. Simulation results validate the model's effectiveness in various scenarios, highlighting its role in refining natural disaster forecasts. [ABSTRACT FROM AUTHOR]

Monitoring the ratio of two correlated normal random variables is often used in many industrial manufacturing processes. At the same time, measurement errors inevitably exist in most processes, which have different effects on the performance of various charting schemes. This paper comprehensively analyses the impacts of measurement errors on the detection ability of the cumulative sum (CUSUM) charting schemes for the ratio of two correlated normal variables. A thorough numerical assessment is performed using the Monte Carlo simulation, and the results indicate that the measurement errors negatively impact the performance of the CUSUM scheme for the ratio of two correlated normal variables. Increasing the number of measurements per set is not a lucrative approach for minimizing the negative impact of measurement errors on the performance of the CUSUM charting scheme when monitoring the ratio of two correlated normal variables. We consider a food formulation as an example that illustrates the quality control problems involving the ratio of two correlated normal variables in an industry with a measurement error. The results are presented, along with some suggestions for further study. [ABSTRACT FROM AUTHOR]

This paper investigates the randomly stopped sums, minima and maxima of heavy- and light-tailed random variables. The conditions on the primary random variables, which are independent but generally not identically distributed, and counting random variable are given in order that the randomly stopped sum, random minimum and maximum is heavy/light tailed. The results generalize some existing ones in the literature. The examples illustrating the results are provided. [ABSTRACT FROM AUTHOR]

This paper describes various selected properties and features of negative binomial (NB) random variables, with special reference to NB2 (i.e., p = 2), and some generalizations to NBp (i.e., p ≥ 2), specifications. It presents new results (e.g., the NBp moment-generating function) with regard to the relationship between a sample mean and its accompanying variance, as well as spatial statistical/econometric numerical and empirical examples, whose parameter estimators are maximum likelihood or method of moment ones. Finally, it highlights the Moran eigenvector spatial filtering methodology within the context of generalized linear modeling, demonstrating it in terms of spatial negative binomial regression. Its overall conclusion is a bolstering of important findings the literature already reports with a newly recognized empirical example of an NB3 phenomenon. [ABSTRACT FROM AUTHOR]

We develop a framework for creating distortion functions that are used to construct new bivariate copulas. It is achieved by transforming non-negative random variables with Lomax-related distributions. In this paper, we apply the distortions to the base copulas of independence, Clayton, Frank, and Gumbel copulas. The properties of the tail dependence coefficient, tail order, and concordance ordering are explored for the new families of distorted copulas. We conducted an empirical study using the daily net returns of Amazon and Google stocks from January 2014 to December 2023. We compared the popular Clayton, Gumbel, Frank, and Gaussian copula models to their corresponding distorted copula models induced by the unit-Lomax and unit-inverse Pareto distortions. The new families of distortion copulas are equipped with additional parameters inherent in the distortion function, providing more flexibility, and are demonstrated to perform better than the base copulas. After analyzing the data, we have found that the joint extremes of Amazon and Google stocks are more likely for high daily net returns than for low daily net returns. [ABSTRACT FROM AUTHOR]

This paper considers three approaches to choosing the constant H in the expression H ⁢ 퐃 ⁢ ζ / n for the error of the Monte Carlo method for numerical calculation of mathematical expectation 퐄 ⁢ ζ of a random variable ζ: in probability, in mean square and in mean.In practical studies using the Monte Carlo method, when estimating the calculation error, it is recommended to use the "in mean" approach with the constant H = 2 π = 0.79788456079 ⁢ ... . [ABSTRACT FROM AUTHOR]

The accurate prediction of short-term platform motions in a real environment is crucial for the safe design, operation, and maintenance of floating offshore wind turbines (FOWTs). Numerical simulations of motions are typically associated with high uncertainties due to abstracted theoretical models, empirical parameters, initial environment parameters, etc. Therefore, it is necessary to integrate other sources of information associated with less uncertainty, e.g., monitoring data, for accurate predictions. In this paper, we propose a probabilistic prediction based on the Bayesian approach that logically integrates motion monitoring data with simulated motion predictions of FOWTs, considering uncertainties in the environment model, structural properties, motion prediction method, monitoring data, etc. The approach consists of constructing a prior probability density function (PDF) of a random variable (which characterizes the largest value of the initial motion response) via numerical simulations and a likelihood function based on platform motion monitoring data and deriving a posterior PDF of the random variable by Bayesian updating. Then, posterior distributions of short-term extreme motion responses are derived using the posterior PDF of the random variable, representing lower uncertainty and improved accuracy. A Metropolis–Hastings algorithm is adopted to obtain PDFs of complex probability distributions. The effectiveness of the approach is demonstrated on a real FOWT platform in Scotland. The proposed probabilistic prediction approach results in posterior distributions of short-term extreme platform motions associated with less uncertainty and higher accuracy, which is attributed to integrating prior knowledge with monitoring data. [ABSTRACT FROM AUTHOR]

The well-known inspection paradox or waiting time paradox states that, in a renewal process, the inspection interval is stochastically larger than a common interarrival time having a distribution function F, where the inspection interval is given by the particular interarrival time containing the specified time point of process inspection. The inspection paradox may also be expressed in terms of expectations, where the order is strict, in general. A renewal process can be utilized to describe the arrivals of vehicles, customers, or claims, for example. As the inspection time may also be considered a random variable T with a left-continuous distribution function G independent of the renewal process, the question arises as to whether the inspection paradox inevitably occurs in this general situation, apart from in some marginal cases with respect to F and G. For a random inspection time T, it is seen that non-trivial choices lead to non-occurrence of the paradox. In this paper, a complete characterization of the non-occurrence of the inspection paradox is given with respect to G. Several examples and related assertions are shown, including the deterministic time situation. [ABSTRACT FROM AUTHOR]

This paper uses a matriceal technique to study properties of the iterates of Mobius transformations when their coefficients are random variables. The algorithms discussed allow to obtain new fractal structures. [ABSTRACT FROM AUTHOR]

This article mainly studies the strong convergence properties for randomly weighted maximum partial sums of arrays of row-wise extended negatively dependent (END, for short) random variables, including the complete moment convergence and complete f-moment convergence. The results obtained in this paper extend the corresponding ones in the literature. As an application, we investigate the complete consistency of the estimators of nonparametric regression models based on END random errors by using the complete convergence that we established. Then we provide comprehensive simulation studies to demonstrate the validity of the theoretical results based on the finite sample performance. Finally, an application to a real data set is illustrated. [ABSTRACT FROM AUTHOR]

In the last two decades, survey researchers have intensively used computerised methods for the collection of different types of paradata, such as keystrokes, mouse clicks and response times, to evaluate and improve survey instruments as well as to understand the survey response process. With the growing popularity of web surveys, the importance of paradata has further increased. Within this context, response time measurement is the prevailing paradata approach. Papers typically analyse the time (measured in milliseconds or seconds) a respondent needs to answer a certain item, question, page or questionnaire. One of the key challenges when analysing the response time is to identify and separate units that are answering too quickly or too slowly. These units can have a poor response quality and are typically labelled as response time outliers. This paper focuses on approaches for identifying and processing response time outliers. It presents a systematic overview of scientific papers on response time outliers in web surveys. The key observed characteristics of the papers are the approaches used, the level of time measurement, the processing of response time outliers and the relationship between response time and response quality. The results show that knowledge on response time outliers is scattered, inconsistent and lacking systematic comparisons of approaches. Consequently, there is a need to improve and upgrade the knowledge on this issue and to develop new approaches that will overcome existing deficiencies and inconsistencies in identifying and dealing with response time outliers. [ABSTRACT FROM AUTHOR]

The takeoff point in this paper is a random variable X for which large positive values are desired. When its probability distribution is highly skewed, the possibility of a long fat-tailed distribution can lead to an expected value, \mu =\mathbb E[ X] , which is unduly optimistic. For the reverse case when small values of X are desired, the ideas in this paper are applied to - X . This issue of over-optimism in the expected value is particularly important when a mission-critical random variable is involved. For example, when considering earthquake intensity or flood levels, reporting an understated expected value to a technically unsophisticated general public would be considered by many as highly undesirable. The Conservative Expected Value (CEV) of X , denoted by \mathbb CEV ( X ) is a new definition provided in this paper. It is a metric which we argue is particularly useful when risk aversion must be highly emphasized. At the same time, while being conservative, the CEV is also aimed at avoiding reflection of excessive pessimism. When, then \mathbb CEV ( X ), while being conservative, is defined in such a way so as not to be unduly pessimistic. In classical analysis, enhancement of a calculation often includes the variance \sigma ^ 2 \,\, = var( X ). However, when large X -values are desired, this may further distort one’s overview of the risk at hand; e.g., if X is profit, values above the mean should not be penalized. With these one-sidedness considerations in mind, we work with a new reward-risk pair, the CEV and the so-called Conservative Semi-Variance (CSV) of X , denoted by \mathbb CSV ( X ). Whereas the CEV definition is entirely new, the CSV definition is motivated by ideas in the area of finance. This paper also illustrates calculation of the CEV and CSV pair for a number of classical probability distributions and includes description of a number of properties of these metrics which suggest that this new theory is mathematically rich. Finally, we demonstrate the potential for application of the theory via two numerical examples. [ABSTRACT FROM AUTHOR]

The present paper is the second part of a series of papers aimed at assessing the accuracy of alchemical computational approaches based on nonequilibrium techniques for solvation free energy of organic molecules in the context of molecular dynamics simulations. In Paper I [Procacci, J. Chem. Phys. 151, 144113 (2019)], we dealt with bidirectional estimates of solvation free energies using nonequilibrium approaches. Here, we assess accuracy and precision of unidirectional estimates with the focus on the Gaussian and Jarzynski estimators. We present a very simple methodology to increase the statistics in the work distribution, hence boosting the accuracy and precision of the Jarzynski unidirectional estimates at no extra cost, exploiting the observed decorrelation between the random variables represented by the Lennard-Jones solute-solvent recoupling or decoupling work and by the electrostatic work due to the charging/discharging of the solute in the solvent. [ABSTRACT FROM AUTHOR]

This paper studies the problem of estimating the covariance of a collection of vectors using only highly compressed measurements of each vector. An estimator based on back-projections of these compressive samples is proposed and analyzed. A distribution-free analysis shows that by observing just a single linear measurement of each vector, one can consistently estimate the covariance matrix, in both infinity and spectral norm, and this analysis leads to precise rates of convergence in both norms. Through information-theoretic techniques, lower bounds showing that this estimator is minimax-optimal for both infinity and spectral norm estimation problems are established. These results are also specialized to give matching upper and lower bounds for estimating the population covariance of a collection of Gaussian vectors, again in the compressive measurement model. The analysis conducted in this paper shows that the effective sample complexity for this problem is scaled by a factor of $m^{2}/d^{2}$ , where $m$ is the compression dimension and $d$ is the ambient dimension. Applications to subspace learning (principal components analysis) and learning over distributed sensor networks are also discussed. [ABSTRACT FROM AUTHOR]

Planning and scheduling approaches in real manufacturing environments entail the need to cope with random attributes and variables to match the characteristics of real scheduling problems where uncertain events are frequent. Moreover, the capability of devising robust schedules, which are less sensitive to the disruptive effects of unexpected events, is a major request in real applications. In this paper, a branch-and-bound approach is proposed to solve the two-machine permutation flow shop scheduling problem with stochastic processing times. The objective is the minimisation of the value-at-risk of the makespan, to support decision-makers in the trade-off between the expected performance and the mitigation of the impact of extreme scenarios. A Markovian Activity Network (MAN) model is adopted to estimate the distribution of the makespan and assess the value-at-risk for both partial and complete schedules. Phase-type distributions are used to enable general distributions for processing times while maintaining the capability to exploit a Markovian approach. The effectiveness and performance of the proposed approach are demonstrated through a set of computational experiments. [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to solve the problem that pipes conveying fluid are faced with severe reliability failures under the complicated working environment. Design/methodology/approach: This paper proposes a dynamic reliability and variance-based global sensitivity analysis (GSA) strategy with non-probabilistic convex model for pipes conveying fluid based on the first passage principle failure mechanism. To illustrate the influence of input uncertainty on output uncertainty of non-probability, the main index and the total index of variance-based GSA analysis are used. Furthermore, considering the efficiency of traditional simulation method, an active learning Kriging surrogate model is introduced to estimate the dynamic reliability and GSA indices of the structure system under random vibration. Findings: The variance-based GSA analysis can measure the effect of input variables of convex model on the dynamic reliability, which provides useful reference and guidance for the design and optimization of pipes conveying fluid. For designers, the rankings and values of main and total indices have essential guiding role in engineering practice. Originality/value: The effectiveness of the proposed method to calculate the dynamic reliability and sensitivity of pipes conveying fluid while ensuring the calculation accuracy and efficiency in the meantime. [ABSTRACT FROM AUTHOR]

This paper provides new insight into the theoretical principle and the practical applicability of the ranked nodes method (RNM) that is used to construct conditional probability tables (CPTs) for Bayesian networks (BNs) by expert elicitation. RNM is designed for specific types of discrete random variables called ranked nodes that are common in real-world applications of BNs. Despite its active use in recent years, there remains ambiguity about the exact theoretical basis of RNM which can hamper its effective employment. In addition, there are a lack of studies about the general ability of CPTs generated with RNM to represent probabilistic relationships in real-world applications. In this paper, it is shown how the generation of probabilities with RNM is underpinned by a regression model of continuous random variables. Then, it is experimentally determined that in typical applications of RNM, one can generate in a matter of seconds CPTs whose elements reflect well probabilities given by the underlying regression model. Another experiment discovers that CPTs generated with RNM provide a good average fit to a large portion of various real-world CPTs investigated. This confirms the usefulness of RNM in practical applications. The results of the experiment also indicate that choices made by the user of RNM can considerably impact the ability of a generated CPT to represent a given probabilistic relationship. This paper then provides practical advice on the efficient use of RNM with regard to the user-controlled features explored in the experiment. [ABSTRACT FROM AUTHOR]

This special issue of the journal is a compilation of papers from the 41 SP st sp IAPSP Annual Conference entitled "Vienna-Kohut-Self Psychology: Searching for Creativity in Times of Crisis." Kottler and Ben co-create a unique, shared visual language in treatment, giving voice to Ben's less articulated and nascent self-states. As they work through their painful encounter, Kottler and Ben confront their largely hidden, alienated alter-ego self-states, "between different parts within a person and between people" (p. 74), which Togashi links to Buber's notion of I-Thou authentic dialogue. [Extracted from the article]

This paper presents secrecy analyses of a full-duplex MIMOME network which consists of two full-duplex multi-antenna users (Alice and Bob) and an arbitrarily located multi-antenna eavesdropper (Eve). The paper assumes that Eve's channel state information (CSI) is completely unknown to Alice and Bob except for a small radius of secured zone. The first part of this paper aims to optimize the powers of jamming noises from both users. To handle Eve's CSI being unknown to users, the focus is placed on Eve at the most harmful location, and the large matrix theory is applied to yield a hardened secrecy rate to work on. The performance gain of the power optimization in terms of maximum tolerable number of antennas on Eve is shown to be significant. The second part of this paper shows two analyses of anti-eavesdropping channel estimation (ANECE) that can better handle Eve with any number of antennas. One analysis assumes that Eve has a prior statistical knowledge of its CSI, which yields lower and upper bounds on secure degrees of freedom of the system as functions of the number (N) of antennas on Eve and the size (K) of information packet. The second analysis assumes that Eve does not have any prior knowledge of its CSI but performs blind detection of information, which yields an approximate secrecy rate for the case of K being larger than N. [ABSTRACT FROM AUTHOR]

For the current problems of complex network state, difficulty in fast response to intrusion and poor adaptation of response decision in fog computing environment, in this paper, we propose an intrusion response decision method based on a combination of deep learning and reinforcement learning based on game theory (Minimax-DQN). First, a Markov game is used as the standard to construct the intrusion response decision model in the fog computing environment. Second, two different sets of random variables are defined considering the possible behavioral choices taken by the attacker and the fog computing intrusion detection systems (FC-IDS), and the continuous state space formed by the game between the attacker and the FC-IDS is processed using a deep Q-network. Finally, the Minimax algorithm is used to solve the optimal value function in a specific state, and the best intrusion response strategy is obtained according to the training output after the training is completed. Three sets of experiments are conducted to compare the results of the Minimax-DQN algorithm, the DQN algorithm and the random strategy. The experimental results data prove that the model and the proposed algorithm can greatly improve the probability of IDS winning in the game process with the attacker, and thus effectively solve the problem of intrusion response decision in fog environment. [ABSTRACT FROM AUTHOR]

In this paper, we estimate the difference |Eh(Zn) −Eh(Y)| between the expectations of real finite Lipschitz function h of the sum Zn = (X1 + ⋯ + Xn)/Bn, where B n 2 = E(X1 + ⋯ + Xn)2> 0, and a standard normal random variable Y, where real centered random variables X1,X2,... satisfy the φ-mixing condition, defined between the "past" and " future", or are m-dependent. In particular cases, under the condition ∑ r = 1 ∞ r φ (r) < ∞ or ∑ r = 1 ∞ r φ 1 / 2 (r) < ∞ , the obtained upper bounds for φ-mixing random variables are of order O(n−1/2). In addition, we refine the previously known upper bounds of order O((m + 1)1+δL2+δ,n), where L2+δ,n is the Lyapunov fraction of order 2 + δ, for m-dependent random variables, supplementing them with explicit constants. We also separately present the case of independent r.v.s. [ABSTRACT FROM AUTHOR]

This paper, which is a continuation of [I. A. Alexeev, Theory Probab. Appl., 67 (2022), pp. 335-351], is concerned with a-stable distributions with complex stability index a. Sufficient conditions for membership in the domain of attraction of a-stable random variables (r.v.'s) are given, and a-stable L'evy processes and the corresponding semigroups of operators are constructed. Necessary and sufficient conditions are given for membership in the class of limit laws for sums of independent and identically distributed (i.i.d.) complex r.v.'s with complex normalization and centering. [ABSTRACT FROM AUTHOR]

Objective: The primary aim of this research paper is to introduce and demonstrate the application of the sine–cosine method and the convolution method for simulating data by utilizing the neutrosophic normal distribution. Method: The methodological framework presented in this paper elaborates on the incorporation of both the sine–cosine method and the convolution method into the realm of neutrosophic statistics. It also introduces algorithms engineered to produce random variables adhering to the neutrosophic normal distribution. Results: Moreover, the study furnishes practical tables that encompass neutrosophic random normal variables generated via the sine–cosine method, as well as tables exhibiting neutrosophic random standard normal variables generated using the convolution method. Conclusion: The analysis undertaken in this study conclusively establishes that the proposed sine–cosine and convolution simulation methods yield outcomes presented in the form of intervals. Furthermore, the study's conclusion emphasizes that the extent of indeterminacy significantly influences the characteristics of the random variates. [ABSTRACT FROM AUTHOR]

In the paper, the complete convergence and complete integral convergence for weighted sums of negatively dependent random variables under the sub-linear expectations are established. The results in the paper extend some complete moment convergence theorems from the classical probability space to the situation of sub-linear expectation space. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the partially linear regression model based on asymptotically almost negatively associated (AANA) random variables. Under some weak conditions, some results of moment convergence and complete convergence are obtained for the parametric least squares estimator and nonparametric weighted estimator. Our results extend the corresponding ones for negatively associated (NA) errors to AANA errors. In addition, we discuss the selection of design points and weight functions. Last, some simulations are illustrated to show the performance of our results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of extended linear negative quadrant dependence (ELNQD, in short). We establish a new concentration inequalities and complete convergence for the distribution of sums of extended linear negative quadrant dependent random variables. Using these inequalities for proved the complete convergence of first autoregressive processes model generated by identically distributed ELNQD errors. [ABSTRACT FROM AUTHOR]

In this paper, we establish a new concentration inequality and almost complete convergence of the value of the process of autoregressive Hilbertian of order one (ARH (1)), which directly stems from works of Serge Guillas, Denis Bosq, that is defined by Xt = ρ(Xt-1) + ζt; t ε ... where the random variables are all Hilbertian, ρ is a linear operator on a space of separable Hilbert and ζt which constitute a widely orthant dependent error (WOD, in short) after recalling some results on the finite-dimensional model of this type, we introduce the mathematical and statistical tools which will be used afterwards. Then we build an estimator of the operator and we establish its asymptotic properties. [ABSTRACT FROM AUTHOR]

We consider random orthonormal polynomials \begin{equation*} F_{n}(x)=\sum _{i=0}^{n}\xi _{i}p_{i}(x), \end{equation*} where \xi _{0}, ..., \xi _{n} are independent random variables with zero mean, unit variance and uniformly bounded (2+\varepsilon) moments, and (p_n)_{n=0}^{\infty } is the system of orthonormal polynomials with respect to a fixed compactly supported measure on the real line. Under mild technical assumptions satisfied by many classes of classical polynomial systems, we establish universality for the leading asymptotics of the average number of real roots of F_n, both globally and locally. Prior to this paper, these results were known only for random orthonormal polynomials with Gaussian coefficients (see D. D. Lubinsky, I. E. Pritsker, and X. Xie [Proc. Amer. Math. Soc. 144 (2016), pp. 1631–1642]) using the Kac-Rice formula, a method that does not extend to the generality of our paper. [ABSTRACT FROM AUTHOR]