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Simulations of condensed matter systems often focus on the dynamics of a few distinguished components but require integrating the full system. A prime example is a molecular dynamics simulation of a (macro)molecule in a solution, where the molecule(s) and the solvent dynamics need to be integrated, rendering the simulations computationally costly and often unfeasible for physically/biologically relevant time scales. Standard coarse graining approaches can reproduce equilibrium distributions and structural features but do not properly include the dynamics. In this work, we develop a general data-driven coarse-graining methodology inspired by the Mori–Zwanzig formalism, which shows that macroscopic systems with a large number of degrees of freedom can be described by a few relevant variables and additional noise and memory terms. Our coarse-graining method consists of numerical integrators for the distinguished components, where the noise and interaction terms with other system components are substituted by a random variable sampled from a data-driven model. The model is parameterized using data from multiple short-time full-system simulations, and then, it is used to run long-time simulations. Applying our methodology to three systems—a distinguished particle under a harmonic and a bistable potential and a dimer with two metastable configurations—the resulting coarse-grained models are capable of reproducing not only the equilibrium distributions but also the dynamic behavior due to temporal correlations and memory effects. Remarkably, our method even reproduces the transition dynamics between metastable states, which is challenging to capture correctly. Our approach is not constrained to specific dynamics and can be extended to systems beyond Langevin dynamics, and, in principle, even to non-equilibrium dynamics. [ABSTRACT FROM AUTHOR]

In practical applications, due to the limited communication bandwidth, the network control systems (NCSs) are prone to data dropouts when the load is high. In this paper, the problem of quantized iterative learning control (ILC) based on encoding and decoding mechanism for such communication-constrained systems is studied. By combining the encoding and decoding mechanism with the uniform quantizer, the network burden and the impact of quantization error on the tracking performance of the systems are significantly mitigated. Meanwhile, data dropouts are represented as the Bernoulli random variable model, and an ILC law based on gradient is designed. When data dropouts occur, the signals maintain the value of the previous trial, otherwise the signals are updated. For this kind of learning framework, the asymptotic zero-error tracking performance has been rigorously proven for the uniform quantizer. To validate the proposed design, a joint motion of an industrial robot in the horizontal plane is simulated as an example. [ABSTRACT FROM AUTHOR]

Most studies for negatively associated (NA) random variables consider the complete-data situation, which is actually a relatively ideal condition in practice. The article relaxes this condition to the incomplete-data setting and considers kernel smoothing density and hazard function estimation in the presence of right censoring based on the Kaplan–Meier estimator. We establish the strong asymptotic properties for these two estimators to assess their asymptotic behavior and justify their practical use. [ABSTRACT FROM AUTHOR]

Let { X n , n ≥ 1 } be a sequence of independent random variables with common general error distribution GED (v) with shape parameter v > 0 , and denote M n and m n the partial maximum and minimum of { X n , n ≥ 1 } . With different normalizing constants, the distributional expansions of normalized sample range M n − m n are established in this article. A byproduct is to deduce the convergence rates of distributions of normalized sample range to their limits, which shows that the optimal convergence rate is proportional to 1 / log n as v ∈ (0 , 1) ∪ (1 , ∞) contrary to the case of v = 1 , which is proportional to 1 / n . Furthermore, numerical analysis is provided to illustrate the theoretical findings. [ABSTRACT FROM AUTHOR]

This article studied a queueing-inventory system with batch demands, randomized order policy, and multiple vacations. Customers arrive in this system according to a Poisson process and take away batch items after a service time. The system sends a replenishment order and starts multiple vacations simultaneously once the on-hand inventory level drops to zero. The replenishment is based on a random order size policy. Customers arriving during this period are assumed to be lost. Under the assumption that all the underlying random variables are exponential, the stationary joint probability is obtained in product form. Based on the stationary distribution, the expected sojourn time of a permitted entering customer is derived in recursive form. Several numerical examples are processed to analyze the effect of variant parameters on the performance measures. The numerical results show that the expected total cost function is a convex function with respect to the maximum allowable inventory. The influence of various parameters on the optimal value is also displayed visually. [ABSTRACT FROM AUTHOR]

This paper studies a general class of social choice problems in which agents' payoff functions (or types) are privately observable random variables, and monetary transfers are not available. We consider cardinal social choice functions which may respond to agents' preference intensities as well as preference rankings. We show that a social choice function is ex ante Pareto efficient and Bayesian incentive compatible if and only if it is dictatorial. The result holds for arbitrary numbers of agents and alternatives, and under a fairly weak assumption on the joint distribution of types, which allows for arbitrary correlations and asymmetries. [ABSTRACT FROM AUTHOR]

In this article, the guaranteed cost control problem for a class of nonlinear networked control systems (NCSs) with dynamic quantization, external bounded disturbance, and data dropout is investigated via the dynamic output feedback. The Takagi–Sugeno (T-S) fuzzy model is used to represent the discrete-time nonlinear system discussed in this paper. Under the dynamic quantization strategy, two quantizers with dynamic parameters are used to quantize the measured output and control input, and the data dropout process is described by introducing the Bernoulli stochastic variable. By using the quadratic boundedness technique, the quadratic stability of the quantized NCS with external disturbance is described. Furthermore, the sufficient condition for the global design approach are proposed, that is, not only the dynamic output feedback controller but parameters of the quantizers are designed synchronously with strict linear matrix inequalities. Eventually, a simulation of nonlinear mass-spring-damper mechanical system is carried out to verify the effectiveness of the provided algorithm. [ABSTRACT FROM AUTHOR]

Generating multivariate normal distributions is widely used in various fields, including engineering, statistics, finance and machine learning. In this paper, simulating large multivariate normal distributions truncated on the intersection of a set of hyperplanes is investigated. Specifically, the proposed methodology focuses on cases where the prior multivariate normal is extracted from a stationary Gaussian process (GP). It is based on combining both Karhunen-Loève expansions (KLE) and Matheron's update rules (MUR). The KLE requires the computation of the decomposition of the covariance matrix of the random variables, which can become expensive when the random vector is too large. To address this issue, the input domain is split in smallest subdomains where the eigendecomposition can be computed. Due to the stationary property, only the eigendecomposition of the first subdomain is required. Through this strategy, the computational complexity is drastically reduced. The mean-square truncation and block errors have been calculated. The efficiency of the proposed approach has been demonstrated through both synthetic and real data studies. [ABSTRACT FROM AUTHOR]

The susceptibility mapping of rainfall-induced landslides is an effective tool for predicting and locating disaster-prone zones at the regional scale. One of the most important parts of landslide susceptibility models is the hydrological model. In this context, the present study considers three pore water pressure (PWP) profiles with surface runoff to estimate the spatiotemporal variation of wetting front depth (WFD) during rainfall episodes. To reasonably simulate the inherent uncertainty and variability involved in the hydrogeomechanical properties of the surficial soil layers at the regional scale, probabilistic analysis based on the recursive first-order reliability method (FORM) is employed to calculate the probability of slope failure. The regional time-dependent landslide susceptibility mapping is realised using a newly developed model called Physically-based probabilistic modelling of Rainfall Landslides using Simplified Transient Infiltration Model (PRL-STIM). The proposed model is applied in a representative area that suffered extensive rainfall-induced landslides in July 2013 (Niangniangba Town, Gansu Province, China). The results indicate that the PRL-STIM model achieved a satisfactory prediction accuracy of 75% AUC compared to existing models like transient rainfall infiltration and grid-based regional slope-stability model (72%) and the probabilistic analysis results based on the first-order second moment method (74%). It also performed well in predicting the spatial distribution of shallow landslides, with a success rate of 81.6%. Regarding the model efficiency, the completion of a raster file for calculating the landslide probabilities of the study area (including 711,051 cells) requires only 17.1 s. It is thus hoped that the proposed calculation framework of PRL-STIM that considers various uncertainties (e.g., nonlinearity of the physical model, non-normal probability distributions, random variable cross correlations, etc.) in geotechnical parameters is better suited for landslide susceptibility mapping at the regional scale, where only limited historical event data is available. [ABSTRACT FROM AUTHOR]

Aero‐disk is a key component of aero‐engine. Due to its complex working conditions, aero‐disk is prone to structural failures. Therefore, it is essential to analyze the reliability and importance input variables of aero‐disk. In this paper, a framework of aero‐disk reliability analysis and global sensitivity analysis (GSA) was established. First, the hazardous regions of aero‐disk were determined by finite element analysis, and the limit state function of aero‐disk was defined by the life interference model. Then D‐Vine model was utilized to establish the correlation model for aero‐disk hazardous regions to evaluate the reliability of aero‐disk. In addition, two GSA methods based on Copula and space partition were proposed to identify important input random variables considering underlying correlation, and the accuracy of the proposed method was verified by two examples. Finally, the proposed method was applied to the GSA of aero‐disk. The results show that the established framework fills in the gap of uncertainty analysis of aero‐disk, which can be extended to other engineering fields. The proposed GSA methods have both high efficiency and accuracy and can realize multi‐dimensional GSA when the correlation of input variables is considered. [ABSTRACT FROM AUTHOR]

The action responses of controlled mechanisms are often multiparametric, nonlinear, and uncertain. Complex dynamics and limited uncertain information pose difficulties for action reliability analysis. This paper develops an adaptive intelligent extremum surrogate model (AIESM) method for the action reliability under random‐interval hybrid uncertainty of a chain conveyor. First, a dynamic model of the chain conveyor is established, which considers the impact and frictional effects within the mechanical system, the regulating effects of the control system, and the external disturbances of the system. After that, a hybrid kernel extreme learning machine optimized by the sparrow search algorithm is employed as an intelligent surrogate model to construct the initial surrogate model from the hybrid uncertain variables to the limit state function (LSF) response and the extremum surrogate model (ESM) from the random variables to the LSF extremum response. An adaptive infilling strategy combining active learning and opposition‐based learning is applied to improve the accuracy and efficiency of the ESM and reduce the estimation error of action reliability. Finally, the action reliability interval bounds are obtained by Monte Carlo simulation based on the ESM. Two numerical examples are presented to illustrate the validity of the AIESM method. The action reliability interval of the chain conveyor provided by the proposed method is [0.9706, 0.9923]. [ABSTRACT FROM AUTHOR]

Let X_1,X_2,\ldots be independent and identically distributed random variables in {\mathbb {C}} chosen from a probability measure \mu and define the random polynomial \begin{align*} P_n(z)=(z-X_1)\ldots (z-X_n)\,. \end{align*} We show that for any sequence k = k(n) satisfying k \leq \log n / (5 \log \log n), the zeros of the kth derivative of P_n are asymptotically distributed according to the same measure \mu. This extends work of Kabluchko, which proved the k = 1 case, as well as Byun, Lee and Reddy [Trans. Amer. Math. Soc. 375, pp. 6311–6335] who proved the fixed k case. [ABSTRACT FROM AUTHOR]

Consider a risk model in which the claims follow a non stationary arrival process that satisfies a large deviation principle. Supposing that the claim sizes form a sequence of i.i.d. random variables with subexponential tail, precise large deviations for the aggregate claims are obtained, by allowing the claim-sizes and claim inter-arrival (waiting) times to be arbitrarily dependent. [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]

Binary classification methods encompass various algorithms to categorize data points into two distinct classes. Binary prediction, in contrast, estimates the likelihood of a binary event occurring. We introduce a novel graphical and quantitative approach, the U-smile method, for assessing prediction improvement stratified by binary outcome class. The U-smile method utilizes a smile-like plot and novel coefficients to measure the relative and absolute change in prediction compared with the reference method. The likelihood-ratio test was used to assess the significance of the change in prediction. Logistic regression models using the Heart Disease dataset and generated random variables were employed to validate the U-smile method. The receiver operating characteristic (ROC) curve was used to compare the results of the U-smile method. The likelihood-ratio test demonstrated that the proposed coefficients consistently generated smile-shaped U-smile plots for the most informative predictors. The U-smile plot proved more effective than the ROC curve in comparing the effects of adding new predictors to the reference method. It effectively highlighted differences in model performance for both non-events and events. Visual analysis of the U-smile plots provided an immediate impression of the usefulness of different predictors at a glance. The U-smile method can guide the selection of the most valuable predictors. It can also be helpful in applications beyond prediction. [ABSTRACT FROM AUTHOR]

In this article, we mainly investigate the complete convergence and complete moment convergence for arrays of rowwise asymptotically almost negatively associated (AANA, in short) random variables. First, some exponential inequalities are presented. By using these inequalities, we establish the complete convergence and complete moment convergence for arrays of rowwise AANA random variables under much weaker conditions. As applications, we provide some corollaries on complete moment convergence for AANA random variables and present an example that satisfies the conditions of the main result. The results obtained in the article generalize and improve some known ones for negatively associated random variables. [ABSTRACT FROM AUTHOR]

In this article, the complete moment convergence for weighted sums of non-identically distributed negatively superadditive dependent (NSD) random variables is investigated. Some sufficient conditions of the complete moment convergence and the complete convergence for the maximum of weighted sums of NSD random variables are established. As applications, some equivalent conditions of the complete moment convergence for a weighted version of NSD cases are presented. Our main results extend and improve the corresponding earlier ones in the literature. [ABSTRACT FROM AUTHOR]

A random effects model for analyzing mixed rank and binomial data with considering the missing values is presented. Occurring of missing data is an important problem in all research fields. The most common approach to dealing with missing data is to delete cases containing missing observations. However, this approach reduces statistical power and mislead us to biased statistical results. This paper aims to prepare guidance for researchers facing missing data problems and to provide techniques for jointly modeling of binomial and rank responses. We compare the cognitive abilities of different primates based on their performance on 17 cognitive assessments obtained on either a rank or binomial scale using Bayesian latent variable with random effects models. Random effects are used to take into account the correlation between responses of the same individual. [ABSTRACT FROM AUTHOR]

In this work, we work on the complete convergence and complete integral convergence for weighted sums for arrays of row-wise widely negative dependent random variables under sub-linear expectation space, promoting the corresponding results from conventional probability space to sub-linear expectation space. This result extends the corresponding outcome obtained by Liang and Wu (2019). [ABSTRACT FROM AUTHOR]

In this article, we mainly study the weak consistency for the Gasser and Müller (G-M) kernel estimator (a weighted kernel estimator with integral form) in a nonparametric regression model based on negatively associated random errors under some suitable conditions. In addition, a simulation to study the numerical performance of the consistency for the G-M estimator is provided. [ABSTRACT FROM AUTHOR]

We obtain strong laws of large numbers of Marcinkiewicz–Zygmund's type for weighted sums of pairwise positively quadrant dependent random variables stochastically dominated by a random variable X ∈ L p , 1 ⩽p < 2. We use our results to establish the strong consistency of estimators which emerge from regression models having pairwise positively quadrant-dependent errors. [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]

The joint analysis of two datasets X and Y that describe the same phenomena (e.g. the cellular state), but measure disjoint sets of variables (e.g. mRNA vs. protein levels) is currently challenging. Traditional methods typically analyze single interaction patterns such as variance or covariance. However, problem-tailored external knowledge may contain multiple different information about the interaction between the measured variables. We introduce MIASA, a holistic framework for the joint analysis of multiple different variables. It consists of assembling multiple different information such as similarity vs. association, expressed in terms of interaction-scores or distances, for subsequent clustering/classification. In addition, our framework includes a novel qualitative Euclidean embedding method (qEE-Transition) which enables using Euclidean-distance/vector-based clustering/classification methods on datasets that have a non-Euclidean-based interaction structure. As an alternative to conventional optimization-based multidimensional scaling methods which are prone to uncertainties, our qEE-Transition generates a new vector representation for each element of the dataset union X∪Y in a common Euclidean space while strictly preserving the original ordering of the assembled interaction-distances. To demonstrate our work, we applied the framework to three types of simulated datasets: samples from families of distributions, samples from correlated random variables, and time-courses of statistical moments for three different types of stochastic two-gene interaction models. We then compared different clustering methods with vs. without the qEE-Transition. For all examples, we found that the qEE-Transition followed by Ward clustering had superior performance compared to non-agglomerative clustering methods but had a varied performance against ultrametric-based agglomerative methods. We also tested the qEE-Transition followed by supervised and unsupervised machine learning methods and found promising results, however, more work is needed for optimal parametrization of these methods. As a future perspective, our framework points to the importance of more developments and validation of distance-distribution models aiming to capture multiple-complex interactions between different variables. [ABSTRACT FROM AUTHOR]

In general, the extended Kalman filter (EKF) has a wide range of applications, aiming to minimize symmetric loss function (mean square error) and improve the accuracy and efficiency of state estimation. As the nonlinear model complexity increases, rounding errors gradually amplify, leading to performance degradation. After multiple iterations, divergence may occur. The traditional extended Kalman filter cannot accurately estimate the nonlinear model, and these errors still have an impact on the accuracy. To improve the filtering performance of the extended Kalman filter (EKF), this paper proposes a new extended Kalman filter (REKF) method that utilizes the statistical properties of the rounding error to enhance the estimation accuracy. After establishing the state model and measurement model, the residual term is used to replace the higher-order term in the Taylor expansion, and the least squares method is applied to identify the residual term step by step. Then, the iterative process of updating the extended Kalman filter is carried out. Within the Kalman filter framework, a higher-order rounding error-based extended Kalman filter (REKF) is designed for the joint estimation of rounding error and random variables, and the solution method for the rounding error is considered for the multilevel approximation of the original function. Through numerical simulations on a general nonlinear model, the higher-order rounding error-based extended Kalman filter (REKF) achieves better estimation results than the extended Kalman filter (EKF) and improves the filtering accuracy by utilizing the higher-order rounding error information, which also proves the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Currently, numerical-simulation-based slope reliability analysis (NSB-SRA) considering spatial variability is still a time-consuming task. To address this problem, this study proposed an efficient numerical-simulation-based slope reliability analysis method. Dual dimensionality reduction technique is firstly employed to greatly reduce random variables that are required for establishing a limit-equilibrium-analysis-based multivariate adaptive regression splines (MARS) model. Then, response conditioning method is used to select the failure samples predicted by MARS model as samples for performing NSB-SRA. Finally, the proposed method is validated through two spatially variable slope examples. The results show that MARS + FDM is an efficient solution to perform NSB-SRA, especially for low-probability-level NSB-SRA problem. Besides, NSB-SRA is necessary for cases of horizontal scale of fluctuation, smaller vertical of fluctuation, larger variability of undrained shear strength, and stronger positive cross-correlation between cohesion and internal friction angle because neglecting NSB-SRA will lead to an unreliable assessment on slope reliability. [ABSTRACT FROM AUTHOR]

The aging intensity (AI), defined as the ratio of the instantaneous hazard rate and a baseline hazard rate, is a useful tool for the describing reliability properties of a random variable corresponding to a lifetime. In this work, the concept of AI is introduced in step-stress accelerated life testing (SSALT) experiments, providing new insights to the model and enabling the further clarification of the differences between the two commonly employed cumulative exposure (CE) and tampered failure rate (TFR) models. New AI-based estimators for the parameters of a SSALT model are proposed and compared to the MLEs in terms of examples and a simulation study. [ABSTRACT FROM AUTHOR]

The effect of pluronics L61 and F68 containing hydrophobic poly(propylene oxide) blocks of the same length and hydrophilic poly(ethylene oxide) blocks of different lengths on the conductance of planar bilayer lipid membranes made of azolectine is investigated. The conductance of these membranes increases as the concentration of both pluronics increases. For the same concentration of pluronics in solution, the conductance is higher for L61. Based on the literature data, the concentration of pluronics bound with the bilayer is calculated. For the close concentration of membrane-bound pluronics, the conductance of membranes is also close. It is concluded that in the first approximation, the appearance of the same hydrophobic parts of pluronics L61 and F68 in a membrane is accompanied by the same increase in its conductance. The conductance vs. concentration curves are superlinear for L61 and sublinear for F68. In the presence of either of these pluronics, the conduction spikes with the amplitude from 10 to 300 pSm and higher are observed for approximately 40% of membranes. These surges of conductance are associated with the appearance of conductive pores or defects in the membrane. The number of pores observed in the membrane is a random variable with a large scatter and does not correlate with the pluronic concentration. The difference between the average pore conductivities for membranes containing L61 and F68 is statistically insignificant. [ABSTRACT FROM AUTHOR]

We study credence goods in a general model. A consumer may suffer a loss which is a continuous random variable. Privately observing the loss value, an expert can provide a repair at a price to eliminate the consumer's loss. All perfect-Bayesian equilibria are inefficient, in that some losses are not repaired. In closed form, we derive a pooling equilibrium (where losses are inferred to be in an interval), and a separating equilibrium (where losses are precisely inferred). If the expert can acquire an information structure on losses, the first best is achieved by a binary signal. Results are robust when cost and loss are random and correlated, and when there are multiple experts. [ABSTRACT FROM AUTHOR]

In this paper, we consider the partial linear regression model yi = xiβ* + g(ti) + εi, i = 1, 2, ..., n, where (xi, ti) are known fixed design points, g(·) is an unknown function, and β* is an unknown parameter to be estimated, random errors εi are (α, β)-mixing random variables. The p-th (p > 1) mean consistency, strong consistency and complete consistency for least squares estimators of β* and g(·) are investigated under some mild conditions. In addition, a numerical simulation is carried out to study the finite sample performance of the theoretical results. Finally, a real data analysis is provided to further verify the effect of the model. [ABSTRACT FROM AUTHOR]

The effects of corrosion in the serviceability state and capacity state on the failure contingency, life cycle cost (LCC) and optimum repair time (ORT) of reinforced concrete beams were evaluated. Gradual corrosion-induced crack widths were obtained using the cohesive crack model. Deterioration of flexural capacity was examined through a simplified three-dimensional finite-element model. Considering the crack width and capacity as random variables in the gamma process, the LCC and ORT were investigated using a renewal process. Analysis of the effective parameters indicated that the corrosion rate in the serviceability state and the tensile rebar ratio in the capacity state had the most significant effects on the probability of failure (PoF), the LCC and the ORT. With a decrease in the corrosion rate, the PoF reduced and the ORT increased. With an increase in the aspect ratio of the section, the LCC increased and the ORT declined. [ABSTRACT FROM AUTHOR]

The anticipative information refers to some information about future events that may be disclosed in advance. This information may regard, for example, financial assets and their future trends. In our paper, we assume the existence of some anticipative information in a market whose risky asset dynamics evolve according to a Brownian motion and a Poisson process. Using Malliavin calculus and filtration enlargement techniques, we derive the information drift of the mentioned processes and, both in the pure jump case and in the mixed one, we compute the additional expected logarithmic utility. Many examples are shown, where the anticipative information is related to some conditions that the constituent processes or their running maximum may verify, in particular, we show new examples considering Bernoulli random variables. [ABSTRACT FROM AUTHOR]

Sequences of discrete random variables are studied whose probability generating functions are zero‐free in a sector of the complex plane around the positive real axis. Sharp bounds on the cumulants of all orders are stated, leading to Berry–Esseen bounds, moderate deviation results, concentration inequalities, and mod‐Gaussian convergence. In addition, an alternate proof of the cumulant bound with improved constants for a class of polynomials all of whose roots lie on the unit circle is provided. A variety of examples is discussed in detail. [ABSTRACT FROM AUTHOR]

A random variable is equi-dispersed if its mean equals its variance. A Poisson distribution is a classical example of this phenomenon. However, a less well-known fact is that the class of normal densities that are equi-dispersed constitutes a one parameter exponential family. In the present article our main focus is on univariate and bivariate models with equi-dispersed normal component distributions. We discuss distributional features of such models, explore inferential aspects and include an example of application of equi-dispersed models. Some related models are discused in Appendices. [ABSTRACT FROM AUTHOR]

We derive new upper bounds for the total variation distance between compound Poisson distributions as well as between a random sum and a compound Poisson distribution, and as a result we also obtain upper bounds for the total variation distance between compound Poisson distributions and a sum of independent random variables. These bounds are generalizations and refinements of some well-known bounds in the literature. We also derive upper bounds for the total variation distance between negative binomial distributions of order k and between the negative binomial distributions of order k and compound Poisson distributions. Upper bounds for the total variation distances between the number of success runs of length k in binary Markovian trials and its limiting distributions for several enumeration schemes, are also given. [ABSTRACT FROM AUTHOR]

Summary: In this article, an event‐triggered recursive filtering problem is studied for a class of nonlinear multi‐rate systems (MRSs) with random transmission delays (RTDs). The RTDs are described by utilizing random variables with a known probability distribution and the Kronecker δ$$ \delta $$ function. To facilitate further study, the MRS is converted into a single‐rate one by adopting an iteration equation approach. To address the challenge of filter design caused by different measurement sampling periods, a modified prediction method of measurements is given. Moreover, an event‐triggered mechanism (ETM) is introduced to regulate the innovation transmission frequency. The objective of the addressed filtering problem is to design a recursive distributed filtering method for MRSs subject to ETM and RTDs, where a minimum upper bound on the filter error covariance is obtained. Moreover, the filter gain matrix is formulated by resorting to the solutions to matrix difference equations. Besides, the boundedness in the mean‐square sense of the filtering error is analyzed and a sufficient condition is provided. Finally, simulations with comparison experiments are presented to demonstrate the effectiveness of the newly proposed theoretical results. [ABSTRACT FROM AUTHOR]

Pore pressure prediction is fundamental when drilling deep and geologically complex reservoirs. Even in relatively well-characterized hydrocarbon reservoir fields, with a considerable number of drilled wells, when located in challenging geological environments, poor prediction of abnormal pore pressure might result in catastrophic events that can cause harm to human lives and infrastructures. To better quantify drilling risks, the uncertainty associated with the pore pressure prediction should be integrated within the geo-modelling workflow. Leveraging a challenging real case from the Brazilian pre-salt, the work presented herein proposes a seismic-driven gradient pore pressure modelling workflow, which combines machine learning and geostatistical co-simulation to predict high-resolution gradient pore pressure volumes. First, existing angle-dependent seismic reflection data are inverted for P- and S-wave velocity and density. Then, K-nearest neighbor is used to create a regression model between pore pressure gradient and P- and S-wave velocity, density and depth based on the well log information. The trained model is applied to predict a three-dimensional gradient pore pressure model from the models obtained from geostatistical seismic inversion. This gradient pore pressure model is a smooth representation of the highly variable subsurface and is used as secondary variable in stochastic sequential co-simulation with joint probability distributions to generate multiple high-resolution realizations of gradient pore pressure. The ensemble of co-simulated models can be used to assess the spatial uncertainty about the gradient pore pressure predictions. The results of the application example show the ability of the method to reproduce the spatial patterns observed in the seismic data and to reproduce existing gradient pore pressure well logs at two blind well locations, which were not used to condition the gradient pore pressure predictions. [ABSTRACT FROM AUTHOR]

In probabilistic coastal hazard assessments based on the Joint Probability Method, historical storm data is used to build distribution models of tropical cyclone atmospheric parameters (i.e., central pressure deficit, forward velocity, radius of maximum wind, and heading direction). Recent models have used a range of assumptions regarding the dependence structure between these random variables. This research investigates the performance of a series of joint distribution models based on assumptions of parameter independence, partial-dependence (i.e., dependence between only central pressure deficit and radius of maximum wind), and full dependence (i.e., dependence between each pair of tropical cyclone atmospheric parameters). Full dependence models consider a range of copula models, such as the Gaussian copula and vine copulas that combine linear-circular copulas with Gaussian or Frank copulas. The consideration of linear-circular copulas allows for the characterization of correlation between linear variables (e.g., central pressure deficit) and circular variables (e.g., heading direction). The sensitivity of the results to different joint distribution models is assessed by comparing hazard curves at representative locations in New Orleans, LA (USA). The stability of hazard curves generated using a Gaussian copula considering variation in the selection of the zero-degree convention is also assessed. The tail dependence between large central pressure deficit and large radius of maximum wind associated with various copula models are also compared using estimated conditional probability. It is found that the linear-circular Frank vine copula model improve the stability of hazard curves and maximize tail dependence between large central pressure deficit and large radius of maximum wind. However, the meta-Gaussian copula model exhibits performance within this study region that was generally consistent with the tested vine copulas and have the advantage of being easier to implement. [ABSTRACT FROM AUTHOR]

Applications of Bayesian updating commonly treat soil parameters as random variables. A significant issue with this is that soil parameters are highly subjective. Therefore, using traditional parameter-based models, Bayesian analysis starts from a subjective prior and it is unclear how this may influence the overall results of a study. In this paper, Bayesian updating is combined with a data-driven method, known as CRACA (i.e., CReep And Consolidation Analysis), for predicting the settlement of embankments on soft soil. Importantly, the method directly ingests measured oedometer data and, therefore, avoids the subjectivity involved in parameter selection. Because parameters are not used, scaling factors are introduced that account uncertainty associated with the laboratory measurements and the automated interpretation process. These factors have an initial value of unity (returning the prior) and are updated in a Bayesian framework as settlement monitoring data are revealed over time to improve future forecasts. The model was applied to an embankment case history and was shown to result in a rapid improvement in the accuracy and a narrowing of the 95% confidence interval as settlement monitoring data are revealed to the model. [ABSTRACT FROM AUTHOR]

We consider computations of Wilson loop expectations to leading order at large β in the case where a non-abelian finite gauge field interacts with a Higgs boson. By identifying the main order contributions from minimal vortices, we can express the Wilson loop expectations via an explicit Poisson random variable. This paper treats multiple cases of interests, including the Higgs boson at low and high disorder, and finds efficient polymer expansion like computations for each of these regimes. [ABSTRACT FROM AUTHOR]

This article introduces a new kind of histogram-based representation for univariate random variables, named the phistogram because of its perceptual qualities. The technique relies on shifted groupings of data, creating a color-gradient zone that evidences the uncertainty from smoothing and highlights sampling issues. In this way, the phistogram offers a deep and visually appealing perspective on the finite sample peculiarities, being capable of depicting the underlying distribution as well, thus, becoming an useful complement to histograms and other statistical summaries. Although not limited to it, the present construction is derived from the equal-area histogram, a variant that differs conceptually from the traditional one. As such a distinction is not greatly emphasized in the literature, the graphical fundamentals are described in detail, and an alternative terminology is proposed to separate some concepts. Additionally, a compact notation is adopted to integrate the representation's metadata into the graphic itself. [ABSTRACT FROM AUTHOR]

The notion of general families of thinning operators is proposed. The main goal of such notion is to allow normalization of integer-valued random variables inside a given class. Some examples of the families of thinning operators are given. [ABSTRACT FROM AUTHOR]

Complex-valued random variables that satisfy usual stability condition for a complex parameter α such that |α − 1/2| < 1/2, are constructed. The characteristic function of the obtained random variables is found and limit theorems for sums of independent identically distributed random variables are proved. The corresponding Lévy processes and semigroups of operators corresponding to these processes are constructed. [ABSTRACT FROM AUTHOR]

This study proposes an efficient reliability updating method to quickly estimate the low-level failure probability, Pf , in structural/geotechnical systems, along with the identification of the most probable failure point (MPP). In this method, Sobol's quasirandom low-discrepancy sequences (LDS) are employed to generate the random samples, and the system reliability updating is conducted based on a weighted low-discrepancy samplings (WLDS) technique. In particular, the updated MPP can be directly captured in x -space according to the probabilistic weighting strategy. Coupled with the copula theory, the implementation framework of the proposed reliability updating method incorporating correlated random variables is thoroughly elaborated. The primary superiority of the proposed reliability updating method with the WLDS technique lies in that the repeated evaluation of costly performance functions is avoided during the updating process. Two illustrative examples show that 2,000 to 20,000 samples are sufficient for estimating and/or updating the probabilistic results of low-level failure probability, Pf , and associated MPP. The proposed method is particularly useful for conducting reliability updating of computationally costly engineering systems in conditions of changing uncertainties such as soil properties, model parameters, and applied structural loadings. [ABSTRACT FROM AUTHOR]

In this paper, we prove an extension of the Jajte weak law of large numbers for exchangeable random variables. We make a simulation to illustrate the asymptotic behavior in the sense of convergence in probability for weighted sums of exchangeable weighted random variables. [ABSTRACT FROM AUTHOR]

Concentration inequalities are widely used tools in many fields such as high-dimensional statistics, machine learning, optimization, signal processing, time series analysis, and finance. Therefore, various types of concentration inequalities have been derived so far. In this study, we derived new concentration inequalities for the sum of subexponential random variables. First one is the concentration inequalities for the sum of subexponential random variables with partial dependence structure. Second one is the concentration inequalities with Pearson's Φ. By applying obtained concentration inequalities to the problem of portfolio risk management, we obtained upper bound for the value-at-risk of financial portfolio. [ABSTRACT FROM AUTHOR]

To monitor the dynamic behavior of degrading systems over time, a flexible hierarchical discrete-time state-space model (SSM) is introduced that can mathematically characterize the stochastic evolution of the latent states (discrete, continuous, or hybrid) of degrading systems, dynamic measurements collected from condition monitoring sources (e.g., sensors with mixed-type outputs), and the failure process. This flexible SSM is inspired by Bayesian hierarchical modeling and recurrent neural networks without imposing prior knowledge regarding the stochastic structure of the system dynamics and its variables. The temporal behavior of degrading systems and the relationship between variables of the corresponding system dynamics are fully characterized by stochastic neural networks without having to define parametric relationships/distributions between deterministic and stochastic variables. A Bayesian filtering-based learning method is introduced to train the structure of the proposed framework with historical data. Also, the steps to utilize the proposed framework for inference and prediction of the latent states and sensor outputs are discussed. Numerical experiments are provided to demonstrate the application of the proposed framework for degradation system modeling and monitoring. [ABSTRACT FROM AUTHOR]

Statistical analysis of samples of the orbits of celestial bodies is complicated by the fact that the Keplerian orbit is a multidimensional object, the coordinate representation of which non-linearly depends on the choice of orbital elements. In this work, using the construction of the Fréchet mean, concepts of mean orbit and dispersion of the orbit family are introduced, consistent with the distance function on the orbit set. The introduced statistical characteristics serve as analogues of sample mean and variance of a one-dimensional random variable. Exact formulas for calculating the elements of mean orbits and dispersion quantities with respect to two metrics on the orbit space are derived. For a large sample of meteoroid orbits from the Geminid stream, numerical simulations of orbit evolution over 20 000 yr in the past were conducted. By analysing the dependency of statistical characteristics on time, estimates for the age of the stream and the gas outflow velocity are obtained under the assumption of the birth of the Geminids due to the rapid destruction of the cometary nucleus. The estimate of the age of the stream lies in the interval from 1200 to 2400 yr, and the speed of gas outflow at perihelion should have been more than 1.2 km s−1. [ABSTRACT FROM AUTHOR]

This study explores a new dimension of accelerated life testing by analyzing competing risk data through Tampered Random Variable (TRV) modeling, a method that has not been extensively studied. This method is applied to simple step-stress life testing (SSLT), and it considers multiple causes of failure. The lifetime of test units under changeable stress levels is modeled using Power Rayleigh distribution with distinct scale parameters and a constant shape parameter. The research introduces unique tampering coefficients for different failure causes in step-stress data modeling through TRV. Using SSLT data, we calculate maximum likelihood estimates for the parameters of our model along with the tampering coefficients and establish three types of confidence intervals under the Type-II censoring scheme. Additionally, we delve into Bayesian inference for these parameters, supported by suitable prior distributions. Our method's validity is demonstrated through extensive simulations and real data application in the medical and electrical engineering fields. We also propose an optimal stress change time criterion and conduct a thorough sensitivity analysis. [ABSTRACT FROM AUTHOR]

The straddle monorail tourist transportation system (MTTS) has developed rapidly in recent years, and its structure is an elevated steel structure with a beam–column system, and the design is executed according to the Safety Code for Large Amusement Rides (GB 8408-2018). However, the impact coefficient value of this code is deemed partially unreasonable. Based on this, relying on the Seven Colors Yunnan Happy World project, the dynamic response test is carried out; using the finite element (FEM) software ANSYS (2021) and multibody dynamics (MBD) software SIMPACK (2021x) combined with the monorail unevenness spectra based on the measured monorail, the straddle monorail vehicle–bridge coupling vibration model is established, and mutual verification is carried out with the measured data. A continuous random variable probability model is adopted for the regularity study of impact coefficient samples, combined with probability statistics and the function fitting method to analyse the calculation results and derive the MTTS displacement impact coefficient calculation formula with beam span and driving speed as variables. The results show that the calculated values of the finite element model are in good agreement with the measured data, and the MTTS impact coefficients conform to the extreme value I-type distribution in the probability distribution law, which is inversely proportional to the span and is directly proportional to the traveling speed. Considering a multi-factor MTTS displacement impact coefficient fitting formula of high fit can better reflect the impact coefficient, monorail girder span, and train speed of the interrelationship for related research and design reference, in order to ensure safety and, at the same time, to improve the economy. [ABSTRACT FROM AUTHOR]

Let { X i , i ≥ 1 } be a sequence of independent and identically distributed random variables with distribution function F and probability density function f. We propose new type of kernel estimators for density and hazard functions that perform well at the boundary, when the variable of interest is positive and right censored. The estimators are constructed using asymmetric kernels with expectation 1. We establish uniform strong consistency rates and we study asymptotic properties and normality of the resulting estimators. A large simulation study is conducted to comfort the theoretical results. An application to real data is done. [ABSTRACT FROM AUTHOR]