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In this paper, we show that a sufficient and necessary condition for that the Hoeffding concentration inequality of Banach space-valued (B -valued, for simplicity) random variables holds is that the Banach space in question admits the Rademacher type p for some 1 ≤ p ≤ 2 ; which is equivalent to that the Bernstein concentration inequality holds for such B -valued random variables. This is done by applying a refined McDiarmid inequality (stated and proved in this paper) via the entropy method. This result is also applied to the density property of induced subgraphs of random Cayley graphs generated by a finite abelian group. [ABSTRACT FROM AUTHOR]

In a recent paper the authors proved a nonuniform local limit theorem concerning normal approximation of the point probabilities P (S = k) when S = ∑ i = 1 n X i and X 1 , X 2 , ... , X n are independent Bernoulli random variables that may have different success probabilities. However, their main result contained an undetermined constant, somewhat limiting its applicability. In this paper we give a nonuniform bound in the same setting but with explicit constants. Our proof uses Stein's method and, in particular, the K-function and concentration inequality approaches. We also prove a new uniform local limit theorem for Poisson binomial random variables that is used to help simplify the proof in the nonuniform case. [ABSTRACT FROM AUTHOR]

This paper provides sets of sufficient conditions for mean convergence theorems for arrays of dependent random variables. We expand and improve a number of particular cases in the literature including Theorem 2.1 in Sung (Appl Math Lett 26(1):18–24, 2013), Theorems 3.1–3.3 in Wu and Guan (J Math Anal Appl 377(2):613–623, 2011), and Theorem 3 in Lita da Silva (Results Math 74(1):1–11, 2019), among others. The proof is different from those in the aforementioned papers and the main results can be applied to obtain mean convergence results for arrays of functions of non-homogeneous Markov chains and dependent bootstrap. [ABSTRACT FROM AUTHOR]

The complementary risk is common and important in the engineering field. However, there is not much research about it because of its complex derivation compared with the competing risk model. In this paper, we concentrate on inference of step-stress partially accelerated life test in the presence of complementary risks under progressive type-II censoring scheme. The Weibull distribution is chosen as the baseline lifetime of the model. The tampered random variable model is adopted as the statistical acceleration model in the accelerated test. We apply both the classical and Bayesian methods to obtain the estimation of lifetime parameters and acceleration factors. The reliability and reversed hazard rate are estimated based on the parametric estimates. The computational formulae of expected total test time are creatively derived under the step-stress and censored setting. The theoretical calculations are compared with simulated values to verify the derivation. Also, numerical studies including the simulation study and real-data analysis in engineering background are conducted to compare and illustrate the performance of the approaches proposed in the paper. Some conclusions and suggestions for actual production are given at the end of the paper. [ABSTRACT FROM AUTHOR]

The framework of this paper was intertemporal choice, that is to say, the process whereby people were required to choose between a smaller-sooner reward and a larger-later income. In this study, the selection of rewards was supported by a discount function instead of direct preferences between the involved rewards. The objective of this paper was to measure the discounting concentration of a discount function through a variant of the Gini index and the Lorenz curve usually used in statistics. Both measures allowed for the comparison of the discounting concentration corresponding to two discount functions. The methodology employed in this paper was based on the parallelism between a discount function and the distribution function of an absolutely continuous random variable. This similarity allowed us to export the measures of concentration from the field of statistics to finance. The main result of this work was the analysis of the discounting concentration depending on other characteristics of the shape of a discount function (regularity and super-additivity) and the total area under the discount function curve. [ABSTRACT FROM AUTHOR]

The article focuses on the system reliability analysis of steel trusses (plane and spatial). The computations are realized by the use of a developed by the author C++ code. The following loads are taken into account: self-weight, weight of coverings, wind and snow. The limit state function is defined as a difference between the bearing capacity and the effect of action of an element. The paper presents how effective tool is the system reliability analysis compared with traditional structural design methods. The methods of transforming Gumbel distribution into normal and generating random variables are described. [ABSTRACT FROM AUTHOR]

Nowadays, one of the main challenges facing green innovation management is how to enhance the performance of innovation processes by utilizing asymmetric input and output data. Therefore, this paper develops an improved SBM model analysis framework for evaluating the green innovation efficiency of asymmetric input and output data. The framework is applied to assess the technical (TE), managerial (PTE), and scale (SE) efficiencies of new energy companies under three input variables (R&D personnel input, R&D capital input, and comprehensive energy consumption input), two desirable output variables (green technology output and economic output), and one undesirable output variable (greenhouse gas emissions). Then, environmental factors and random factors are eliminated from the obtained input slack variables based on the SFA model, placing decision-making units in a homogeneous environment. The results demonstrate that TE, PTE, and SE are improved after eliminating environmental factors and random factors. Subsequently, based on the entropy method, this paper classifies companies' green innovation patterns into four categories and provides targeted solutions. The purpose of this paper is to provide an evaluation method for new energy companies to understand green innovation efficiency and assist decision makers in identifying the most optimal resource allocation approach. The proposed improved SBM model contributes to the literature and to industry practice by (1) providing a reliable evaluation of green innovation efficiency under asymmetric input and output data; (2) determining effective improvement actions based on a slack analysis of environmental variables and random variables that lead to improved process performance; and (3) making fuzzy innovation performance efficient to facilitate understanding and managing innovation resource allocation quality. [ABSTRACT FROM AUTHOR]

We would like to point out that the formula for the cumulative distribution given in Coelho-Barros et al. (2017) and a similar version of it given in Usman et al. (2021) are not cumulative distribution functions as these functions do not satisfy the one or more necessary and sufficient conditions for a function to be a cumulative distribution function. We would also like to mention that formulas for the cumulative distribution functions of product and ratio of two independent Pareto and Exponential random variables given by Obeid and Kadry (2022) are not cumulative distribution functions either. We do not believe that these formulas can be fixed to be cumulative distribution functions. In this short article, we provide mathematical justification in support of these claims. [ABSTRACT FROM AUTHOR]

This scientific paper explores the operation of a multiprocessor task servicing system. Tasks are received into the system at random intervals and are characterized by several stochastic parameters, including the number of processors required for their execution, the maximum allowable busy time for these processors, and the permissible waiting time in the task queue. The organization of task servicing in this system follows a first-in, first-out (FIFO) approach, ensuring uninterrupted processing. The key servicing process involves periodically selecting the first task in the queue and assessing its feasibility for immediate execution. If the task meets the necessary criteria, it is dispatched for processing. This process continues iteratively until a task is found, the parameters of which prevent immediate servicing. It is important to note that tasks in the queue have a limited window of time within which they can be serviced; otherwise, they may exit the system without service. This paper focuses on systems characterized by exponential distributions for random variables related to task arrivals, servicing times, and waiting restrictions. A system of equations is derived that describes the system's steady-state behavior. These equations enable the calculation of probabilities associated with the system's various states. Additionally, the paper provides insights into the probability distributions of virtual waiting times for tasks that arrive in the system at any given moment. [ABSTRACT FROM AUTHOR]

The maximal positive I I i I k i identifies the variables that co-vary the most in the population, whereas the minimal negative I I i I k i identifies synergistic clusters and the variables that differentiate-segregate the most in the population. Detailed state variables are reduced using the usual principle of maximum entropy (MaxEnt), whereas relaxation of the conjugate variables guarantees that the reduced equations are closed. Pursuing the work of Hu Kuo Ting and Te Sun Han, we show that information functions provide coordinates for binary variables and that they are analytically independent of the probability simplex for any set of finite variables. [Extracted from the article]

Consider a multidimensional risk model, in which an insurer is exposed to more than one type of claims sharing a common accident-number process, and each type of the individual claims and the accident inter-arrival times are, respectively, extended negatively dependent and identically distributed nonnegative random variables. In various insurance contexts, it is hard to assume some specific dependence between the claims and the inter-arrival times due to their complex interplay, and hence arbitrary dependence is allowed in this paper. Under the assumption of the individual claims possessing dominatedly varying tails and some moment condition on the inter-arrival times, this paper establishes a precise large deviation result for the aggregate claim vector. [ABSTRACT FROM AUTHOR]

This paper studies the downlink of a cloud radio access network (C-RAN) in which a centralized processor (CP) communicates with mobile users through base stations (BSs) that are connected to the CP via finite-capacity fronthaul links. Information theoretically, the downlink of a C-RAN is modeled as a two-hop broadcast-relay network. Among the various transmission and relaying strategies for such model, this paper focuses on the compression strategy, in which the CP centrally encodes the signals to be broadcast jointly by the BSs, then compresses and sends these signals to the BSs through the fronthaul links. We characterize an achievable rate region for a generalized compression strategy with Marton’s multicoding for broadcasting and multivariate compression for fronthaul transmission. We then compare this rate region with the distributed decode-forward (DDF) scheme, which achieves the capacity of the general relay networks to within a constant gap, and show that the difference lies in that DDF performs Marton’s multicoding and multivariate compression jointly as opposed to successively as in the compression strategy. A main result of this paper is that under the assumption that the fronthaul links are subject to a sum capacity constraint, this difference is immaterial; so, for the Gaussian network, the compression strategy based on successive encoding can already achieve the capacity region of the C-RAN to within a constant gap, where the gap is independent of the channel parameters and the power constraints at the BSs. As a further result, for C-RAN under individual fronthaul constraints, this paper also establishes that the compression strategy can achieve to within a constant gap to the sum capacity. [ABSTRACT FROM AUTHOR]

Discusses the multivariate extreme value theory that emerged in several studies in the 1950s during the popularity of asymptomatic distributions in probability. Examination on the mathematical abstraction of the formulation of the theory; Discovery of the deficiencies of this appraoch during the 1990s; Information on proposed correction to the deficiencies of the approach.

In this paper we consider two random variables in a cell in the network of mobile users. The first random variable (RV) is the distance of active mobile user from a base station. The second RV is emission power for the random active user if the control of emission power exists. RV emission power is dependent RV of the first RV. That's why the calculations of mean values for these RVs differ one from the other. The first RV depends only on the users' density area distribution. The second RV depends on the signal attenuation value in the considered environment. It is proved that, in real conditions, emission power to a user at the mean value of distance from a base station is always lower than mean value of emission power to a user. The difference between these two power values increases as the signal attenuation coefficient increases. These two values are calculated for three characteristic user density distributions in a cell. The results are verified by original computer simulation programs. [ABSTRACT FROM AUTHOR]

Dynamic reliability evaluation of large-scale reinforced concrete (RC) structures is one of the most challenging problems in engineering practices. Although extensive endeavors have been devoted to mechanical analysis of concrete structures in the past decades, it was recognized that the randomness from both structural parameters and excitations have significant effects on the dynamic behaviors of structures with complex nonlinearity, damage, energy dissipation, and plasticity. Thus, great difficulty exists in evaluating the nonlinear stochastic responses and dynamic reliability of the real-world complex structures of large degrees of freedom. In the present paper, a physically driven method for refined probabilistic response and seismic reliability evaluation of real-world RC structures is proposed via synthesis of the refined mechanical analysis and the physically-based uncertainty propagation. In this method, the material parameters can be treated as probabilistically dependent random variables characterized by vine copulas, and the ground motion is modeled by non-stationary Clough–Penzien spectrum. The uncertainty propagation of arbitrary response quantity(-ies) of interest is governed by the dimension-reduced probability density evolution equation (DR-PDEE). The intrinsic drift coefficients in the DR-PDEE are the physically driven force for the uncertainty propagation and can be identified via data from representative dynamic analyses of the structure. The time-variant reliability of the structures can be captured by solving the physically driven DR-PDEE, which cannot be achieved by the general Monte Carlo simulation (MCS) due to the prohabitively large computational cost. Finally, a practical engineering application is shown in this paper for the probabilistic response and seismic reliability evaluation of a 24-story RC shear wall structure with nearly 280,000 degrees of freedom (DOFs). [ABSTRACT FROM AUTHOR]

This paper introduces a novel three-parameter skew-log-logistic distribution. The research involves the development of a new random variable based on Azzalini and Capitanio's (2013) proposition. Additionally, various statistical properties of this distribution are explored. The paper presents a maximum likelihood method for estimating the distribution's parameters. The density function exhibits unimodality with heavy right tails, while the hazard function exhibits rapid increase, unimodality, and slow decrease, resulting in a right-skewed curve. Furthermore, four real datasets are utilized to assess the applicability of this new distribution. The AIC and BIC criteria are employed to assess the goodness of fit, revealing that the new distribution offers greater flexibility compared to the baseline distribution. [ABSTRACT FROM AUTHOR]

In this paper, we find conditions under which distribution functions of randomly stopped minimum, maximum, minimum of sums and maximum of sums belong to the class of generalized subexponential distributions. The results presented in this article complement the closure properties of randomly stopped sums considered in the authors' previous work. In this work, as in the previous one, the primary random variables are supposed to be independent and real-valued, but not necessarily identically distributed. The counting random variable describing the stopping moment of random structures is supposed to be nonnegative, integer-valued and not degenerate at zero. In addition, it is supposed that counting random variable and the sequence of the primary random variables are independent. At the end of the paper, it is demonstrated how randomly stopped structures can be applied to the construction of new generalized subexponential distributions. [ABSTRACT FROM AUTHOR]

In this paper we use the Riemann zeta distribution to give a new proof of the Erdös-Kac Central Limit Theorem. That is, if \zeta (s)=\sum _{n\ge 1} \frac {1}{n^s}, s>1, then we consider the random variable X_s with P(X_s=n)=\frac {1}{\zeta (s)n^s}, n\ge 1. In an earlier paper, the first author and Adrien Peltzer derived the analog of the Erdös-Kac Central Limit Theorem (CLT) for the number of distinct prime factors, \omega (X_s), of X_s, as s\searrow 1. In this paper we show, by means of a Tauberian Theorem, how to obtain the Central Limit Theorem of Erdös-Kac for the uniform distribution from the result for the random variable X_s. We also apply the technique to the number of distinct prime divisors of X_s that lie in an arithmetic sequence and a local CLT of the type proved by Dixit and Murty [Hardy-Ramanujan J. 43 (2020), 17–23] as well a version of the CLT for irreducible divisors of a monic polynomial over a finite field. [ABSTRACT FROM AUTHOR]

U-statistics represent a fundamental class of statistics arising from modeling quantities of interest defined by multi-subject responses. U-statistics generalize the empirical mean of a random variable X to sums over every m-tuple of distinct observations of X. Stute [182] introduced a class of so-called conditional U-statistics, which may be viewed as a generalization of the Nadaraya-Watson estimates of a regression function. Stute proved their strong pointwise consistency to: r(m)(φ, t) ≔ 피[φ(F1,..., Ym)|(X1,..., Xm) = t], for t ∈ Xm. In this paper, we are mainly interested in the study of the kNN conditional U-processes in a functional mixing data framework. More precisely, we investigate the weak convergence of the conditional empirical process indexed by a suitable class of functions and of the kNN conditional U-processes when the explicative variable is functional. We treat the uniform central limit theorem in both cases when the class of functions is bounded or unbounded satisfying some moment conditions. The second main contribution of this study is the establishment of a sharp almost complete Uniform consistency in the Number of Neighbors of the constructed estimator. Such a result allows the number of neighbors to vary within a complete range for which the estimator is consistent. Consequently, it represents an interesting guideline in practice to select the optimal bandwidth in nonparametric functional data analysis. These results are proved under some standard structural conditions on the Vapnik-Chervonenkis classes of functions and some mild conditions on the model. The theoretical results established in this paper are (or will be) key tools for further functional data analysis developments. Potential applications include the set indexed conditional U-statistics, Kendall rank correlation coefficient, the discrimination problems and the time series prediction from a continuous set of past values. [ABSTRACT FROM AUTHOR]

Frequent natural disasters challenge relief network efficiency. This paper introduces a stochastic relief network with limited path capacity, develops an equilibrium model based on cumulative prospect theory, and formulates it as a stochastic variational inequality problem to enhance emergency response and resource allocation efficiency. Using the NCP function, Lagrange function, and random variables, the model dynamically monitors disasters, enabling rational resource allocation for quick decision-making. Compared to traditional methods, our model significantly improves resource scheduling and reduces disaster response costs. Through a random network example, we validate the model's effectiveness in aiding intelligent decision-making for relief plans and resource allocation optimization. [ABSTRACT FROM AUTHOR]

This paper discusses the dissipative filtering problem for discrete-time nonlinear networked systems with dynamic quantization and data packet dropouts. The Takagi–Sugeno (T–S) fuzzy model is employed to approximate the considered nonlinear plant. Both the measurement and performance outputs are assumed to be quantized by the dynamic quantizers before being transmitted. Moreover, the Bernoulli stochastic variables are utilized to characterize the effects of data packet dropouts on the measurement and performance outputs. The purpose of this paper is to design full- and reduced-order filters, such that the stochastic stability and dissipative filtering performance for the filtering error system can be guaranteed. The collaborative design conditions for the desired filter and the dynamic quantizers are expressed in the form of linear matrix inequalities. Finally, simulation results are used to illustrate the feasibility of the proposed filtering scheme. [ABSTRACT FROM AUTHOR]

In the paper, we establish the complete convergence for weighted sums of random variables satisfying generalized Rosenthal-type inequalities. Our results partially extend some known results and weaken their conditions. As statistical applications, we study the nonparametric regression model and obtain the complete consistency of the weighted regression estimator for the unknown regression functions. [ABSTRACT FROM AUTHOR]

Let X1, X2, . . ., Xn be a sequence of coherent random variables, i.e., satisfying the equalities Xj = P(A|Gj), j = 1, 2, . . ., n, almost surely for some event A. This paper contains the proof of the estimate P (max 1=i

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In recent years, uncertainty analysis is a hot topic in the field of electromagnetic compatibility simulation. The actual electromagnetic environment is simulated by considering the randomness of the model input parameters. However, there are currently two key issues that have not been resolved. One is the curse of dimensionality problem that occurs when there are many random variables. The other is how to establish a random input model with generality and portability. In order to address these issues, this paper proposes a new random input modeling method called random variable black box model. When applying to the Stochastic Collocation Method with dimensionality reduction sparse grid strategy, the applicability of this uncertainty analysis method can be extended to any probability density function, then enabling efficient electromagnetic compatibility simulation uncertainty analysis of high-dimensional random variable models and fundamentally solving the curse of dimensionality problem. Finally, this paper implements a joint simulation technology of the MATLAB software and COMSOL software to verify the strong portability of the random variable black box model, ensuring that advanced uncertainty analysis methods can be smoothly introduced into commercial electromagnetic simulation software and expanding the application scope of uncertainty analysis. [ABSTRACT FROM AUTHOR]

In this paper, the asmptotics is considered for the distribution tail of a randomly stopped sum Sν = X1 + ··· + Xν of independent identically distributed consistently varying random variables with zero mean, where ν is a counting random variable independent of {X1,X2, . . .}. The conditions are provided for the relation P(Sν > x) ∼ Eν P(X1 > x) to hold, as x →∞, involving the finiteness of E|X1|. The result improves that of Olvera-Cravioto [14], where the finiteness of a moment E|X1|r for some r > 1 was assumed. [ABSTRACT FROM AUTHOR]

We propose a successive cancellation list (SCL) encoding and decoding scheme for the Gelfand Pinsker (GP) problem based on the known nested polar coding scheme. It applies SCL encoding for the source coding part, and SCL decoding with a properly defined CRC for the channel coding part. The scheme shows improved performance compared to the existing method. A known issue with nested polar codes for binary dirty paper is the existence of frozen channel code bits that are not frozen in the source code. These bits need to be retransmitted in a second phase of the scheme, thus reducing the rate and increasing the required blocklength. We provide an improved bound on the size of this set, and on its scaling with respect to the blocklength, when the Bhattacharyya parameter of the test channel used for source coding is sufficiently large, or the Bhattacharyya parameter of the channel seen at the decoder is sufficiently small. The result is formulated for an arbitrary binary-input memoryless GP problem, since unlike the previous results, it does not require degradedness of the two channels mentioned above. Finally, we present simulation results for binary dirty paper and noisy write once memory codes. [ABSTRACT FROM AUTHOR]

This paper will be devoted to the study of weighted (deformed) free Poisson random variables from the viewpoint of orthogonal polynomials and statistics of non-crossing partitions. A family of weighted (deformed) free Poisson random variables will be defined in a sense by the sum of weighted (deformed) free creation, annihilation, scalar, and intermediate operators with certain parameters on a weighted (deformed) free Fock space together with the vacuum expectation. We shall provide a combinatorial moment formula of non-commutative Poisson random variables. This formula gives us a very nice combinatorial interpretation to two parameters of weights. One can see that the deformation treated in this paper interpolates free and boolean Poisson random variables, their distributions and moments, and yields some conditionally free Poisson distribution by taking limit of the parameter. [ABSTRACT FROM AUTHOR]

Traditionally, the reliability of a rock slope is evaluated based on the linear Mohr–Coulomb strength criterion, neglecting the nonlinear shear strength of the majority of geotechnical materials. The paper proposes a probability method to assess the reliability of rock slopes based on the power-type nonlinear strength criterion and the mean-value first-order second-moment method. In the proposed method, a novel analytical method to determine the safety factors of slopes with plane failure is derived based on the power-type nonlinear strength criterion. The local mean value of a random variable on the failure surface is determined based on the two-dimensional random field theory, avoiding the random field simulation. To quickly search the minimum reliability index βmin, a dichotomic search method is proposed. The validity of the proposed method is demonstrated in two cases. The study results from the two cases illustrate that the proposed method has high computational efficiency and accuracy. The proposed method offers a fresh way to examine the reliability of rock slopes when the nonlinear strength criterion is adopted. [ABSTRACT FROM AUTHOR]

To ensure the efficient functioning of solar energy generation systems, it is crucial to have dependable designs and regular maintenance. However, when these systems or their components operate at multiple working levels, optimizing reliability becomes a complex task for models and analyses. In the context of reliability modeling in solar energy generation systems, researchers often assume that random variables follow an exponential distribution (binary-state representation) as a simplification, although this may not always hold true for real-world engineering systems. In the present paper, a multi-state solar energy generating system with inverters in series configuration is investigated, in which unreliable by-pass changeover switches, common cause failures (CCFs), and multiple repairman vacations are also considered. Furthermore, the arrivals of CCFs and the repair processes of the failed system due to CCFs are governed by different Markovian arrival processes (MAPs), and the lifetimes and repair times of inverters and by-pass changeover switches and the repairman vacation time in the system have different phase-type (PH) distributions. Therefore, the behavior of the system is represented using a Markov process methodology, and reliability measures for the proposed system are derived utilizing aggregated stochastic process theory. Finally, a numerical example and a comparison analysis are presented to demonstrate the findings. [ABSTRACT FROM AUTHOR]

Background: Simulation is an important tool for assessing the performance of statistical methods for the analysis of data and for the planning of studies. While methods are available for the simulation of correlated binary random variables, all have significant practical limitations for simulating outcomes from longitudinal cluster randomised trial designs, such as the cluster randomised crossover and the stepped wedge trial designs. For these trial designs as the number of observations in each cluster increases these methods either become computationally infeasible or their range of allowable correlations rapidly shrinks to zero. Methods: In this paper we present a simple method for simulating binary random variables with a specified vector of prevalences and correlation matrix. This method allows for the outcome prevalence to change due to treatment or over time, and for a 'nested exchangeable' correlation structure, in which observations in the same cluster are more highly correlated if they are measured in the same time period than in different time periods, and where different individuals are measured in each time period. This means that our method is also applicable to more general hierarchical clustered data contexts, such as students within classrooms within schools. The method is demonstrated by simulating 1000 datasets with parameters matching those derived from data from a cluster randomised crossover trial assessing two variants of stress ulcer prophylaxis. Results: Our method is orders of magnitude faster than the most well known general simulation method while also allowing a much wider range of correlations than alternative methods. An implementation of our method is available in an R package NestBin. Conclusions: This simulation method is the first to allow for practical and efficient simulation of large datasets of binary outcomes with the commonly used nested exchangeable correlation structure. This will allow for much more effective testing of designs and inference methods for longitudinal cluster randomised trials with binary outcomes. [ABSTRACT FROM AUTHOR]

In this paper, we generalize two new statistical distributions, to improve the ability to model failure rates with non-monotonic, monotonic, and mainly bathtub curve behaviors. We call these distributions Generalized Powered Uniform Distribution and MOE-Powered Uniform. The proposed distributions' approach is based on incorporating a parameter k in the power of the values of the random variables, which is associated with the Probability Density Function and includes an operator called the Powered Mean. Various statistical and mathematical features focused on reliability analysis are presented and discussed, to make the models attractive to reliability engineering or medicine specialists. We employed the Maximum Likelihood Estimator method to estimate the model parameters and we analyzed its performance through a Monte Carlo simulation study. To demonstrate the flexibility of the proposed approach, a comparative analysis was carried out on four case studies with the proposed MOE-Powered Uniform distribution, which can model failure times as a bathtub curve. The results showed that this new model is more flexible and useful for performing reliability analysis. [ABSTRACT FROM AUTHOR]

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]

The complete characterization of the almost-entropic region yields rate regions for network coding problems. However, this characterization is difficult and open. In this paper, we propose a novel algorithm to determine whether an arbitrary vector in the entropy space is entropic or not, by parameterizing and generating probability mass functions by neural networks. Given a target vector, the algorithm minimizes the normalized distance between the target vector and the generated entropic vector by training the neural network. The algorithm reveals the entropic nature of the target vector, and obtains the underlying distribution, accordingly. The proposed algorithm was further implemented with convolutional neural networks, which naturally fit the structure of joint probability mass functions, and accelerate the algorithm with GPUs. Empirical results demonstrate improved normalized distances and convergence performances compared with prior works. We also conducted optimizations of the Ingleton score and Ingleton violation index, where a new lower bound of the Ingleton violation index was obtained. An inner bound of the almost-entropic region with four random variables was constructed with the proposed method, presenting the current best inner bound measured by the volume ratio. The potential of a computer-aided approach to construct achievable schemes for network coding problems using the proposed method is discussed. [ABSTRACT FROM AUTHOR]

The probabilistic seismic demand model (PSDM) is essential to identify the seismic demand of the highway bridge during and after an earthquake. This paper aims to review the probabilistic seismic demand estimation and modeling methodology options associated with the procedure, analytical analysis, and mathematical framework for a highway bridge. As a result of the review, different techniques with features, applications, and limitations on highway bridges are reviewed and presented. A review has investigated the current PSDM and provides a comprehensive summary with formulas, tables, figures, and frameworks. PSDM steps are constructed and introduced to how scholars use them. Besides, analytical methods are the best choice for investigating the PSDA and PSDM for critical bridge components when damage data is insufficient. They are determined to predict each component's seismic response for a given deterministic or random variable. This work helps and motivates the decision-makers and stakeholders to extend the application of the PSDM methodology option for a more informed decision. [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]

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]

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]

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 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]

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]

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]

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]