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While the linear Pearson correlation coefficient represents a well-established normalized measure to quantify the inter-relation of two stochastic variables X and Y, it fails for multidimensional variables, such as Cartesian coordinates. Avoiding any assumption about the underlying data, the mutual information I(X, Y) does account for multidimensional correlations. However, unlike the normalized Pearson correlation, it has no upper bound (I ∈ [0, ∞)), i.e., it is not clear if say, I = 0.4 corresponds to a low or a high correlation. Moreover, the mutual information (MI) involves the estimation of high-dimensional probability densities (e.g., six-dimensional for Cartesian coordinates), which requires a k nearest-neighbor algorithm, such as the estimator by Kraskov et al. [Phys. Rev. E 69, 066138 (2004)]. As existing methods to normalize the MI cannot be used in connection with this estimator, a new approach is presented, which uses an entropy estimation method that is invariant under variable transformations. The algorithm is numerically efficient and does not require more effort than the calculation of the (un-normalized) MI. After validating the method by applying it to various toy models, the normalized MI between the Cα-coordinates of T4 lysozyme is considered and compared to a correlation analysis of inter-residue contacts. [ABSTRACT FROM AUTHOR]

We consider a production-inventory system in which the facility produces continuously, switching between two production rates: one faster and one slower than the average demand rate. Demand follows a compound Poisson process, and the size of each demand request is an exponential random variable. Unsatisfied demand is backordered. The production-inventory system is controlled by a two-critical number policy (r, R), whereby production switches from the slower rate to the faster rate when inventory drops below level r and from the faster rate to the slower rate when inventory reaches level R. A fixed cost occurs whenever production switches rates. Our analysis covers two cases: r ≥ 0 and the less studied case of r ≤ 0. We use a level crossing approach to derive the steadystate distribution of the inventory level. Using the steady-state distribution of the inventory level, we calculate the total expected inventory holding, backorder, and switchover costs for each of the two cases. We outline how to obtain the optimal policy through a search of the expected cost functions. We also propose heuristics that give simple closed-form solutions with near-optimal performance. Through a numerical study, we illustrate the importance of considering the r ≤ 0 case. [ABSTRACT FROM AUTHOR]

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

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]

This article considers wavelet estimations for density functions in Besov spaces based on negatively dependent biased random samples. More precisely, wavelet estimators are defined and their L p (1 ≤ p < ∞) convergence rates are provided when the parameter μ is known and unknown, respectively. [ABSTRACT FROM AUTHOR]

This article is devoted towards some necessary conditions for the existence of the mild solution of 'second‐order semilinear stochastic delay differential equations' having a variable delay in the state with the help of Banach fixed point theorem and theory of cosine family which is strongly continuous. In the last section, we have discussed an example to understand the theory of provided results in a better manner. [ABSTRACT FROM AUTHOR]

Here, we solve an open problem raised by Harkness and Shantaram in 1969 who obtained, under sufficient conditions, a limit theorem in law for sequences of nonnegative random variables built with the iterated stationary excess operator. More precisely, they considered the distribution function (d.f.) F of a nonnegative random variable X having all moments μn=∫0∞undF(u) finite. The stationary excess operator corresponds to the d.f. F1(x)=μ1−1∫0x1−F(u)du,x>0, so that the iterated stationary excess operator (ISEO) at the order n ≥ 2 corresponds to the d.f. Fn(x)=μ1,n−1−1∫0x1−Fn−1(u)du, where μ1,n−1=∫0∞1−Fn−1(u)du. Let the r.v. En(X) denotes a realization of Fn. Harkness and Shantaram provided sufficient conditions for the existence of a normalizing sequence cn such that the sequence En(X)/cn converges in distribution or, equivalently, Fn(cnx) → G(x) for some d.f. G. This raises a problem of identification the class of possible limits G. We give here a complete answer to this problem through the convergence of families built by the continuous time version of the ISEO and also by size biasing. In this context, we show that (i)the conditions of Harkness and Shantaram are actually necessary;(ii)continuous time convergence is equivalent to discrete time convergence; and(iii)the only possible limits in distribution G are mixture of exponential with log‐normal distributions. [ABSTRACT FROM AUTHOR]

Stochastic modelling of fatigue (and other material's deterioration), as well as of cumulative damage in risk theory, are often based on compound sums of independent random variables, where the number of addends is represented by an independent counting process. We consider here a cumulative model where, instead of a renewal process (as in the Poisson case), a linear birth (or Yule) process is used. This corresponds to the assumption that the frequency of "damage" increments accelerates according to the increasing number of "damages". We start from the partial differential equation satisfied by its transition density, in the case of exponentially distributed addends, and then we generalize it by introducing a space derivative of convolution type (i.e., defined in terms of the Laplace exponent of a subordinator). Then we are concerned with the solution of integro‐differential equations, under proper initial conditions, which, in a special case, reduce to a fractional one. Correspondingly, we analyze the related cumulative jump processes under a general infinitely divisible distribution of the (positive) jumps. Some special cases (such as the stable, tempered stable, gamma, and Poisson) are presented. [ABSTRACT FROM AUTHOR]

This article presents an adaptive control algorithm for stochastic nonholonomic systems subject to state constraints and input saturation simultaneously. We give a state‐input scaling transformation and a novel auxiliary variable to transform the stochastic nonholonomic system into a new one to make it easier to design the controller, and adopt a switching strategy to eliminate the phenomenon of uncontrollability. By introducing a barrier Lyapunov function and defining a suitable adaptive parameter, we construct a novel adaptive neural network controller with only one adaptive law, which can alleviate computation burden. The presented controller not only overcomes the effects of both full‐state constraints and full‐input saturation on system performance, but also ensures that all states of the closed‐loop are semi‐globally uniformly ultimately bounded in probability. Additionally, all state variables are restricted to the predefined compact sets. Finally, an example is used to validate the efficacy of the established controller. [ABSTRACT FROM AUTHOR]

In this paper, random and stochastic processes are defined on fractal curves. Fractal calculus is used to define the cumulative distribution function, probability density function, moments, variance, and correlation function of stochastic processes on fractal curves. A new framework, which is a generalization of mean square calculus, is formulated. The sequence of random variables on the fractal curve, fractal mean square continuity, mean square F α -derivative, and fractal mean square integral are discussed. The mean square solution of a fractal stochastic equation is derived and plotted to illustrate the details. [ABSTRACT FROM AUTHOR]

Using scenarios to model a stochastic system's behavior poses a dilemma. While a large(r) set of scenarios usually improves the model's accuracy, it also causes drastic increases in the model's size and the computational effort required. Multi-period descriptive sampling (MPDS) is a new way to generate a small(er) set of scenarios that yield a good fit both to the periods' probability distributions and to the convoluted probability distributions of stochastic variables (e.g., period demands) over time. MPDS uses descriptive sampling to draw a sample of S representative random numbers from a period's known (demand) distribution. Now, to create a set of S representative scenarios, MPDS heuristically combines these random numbers (period demands) period by period so that a good fit is achieved to the convoluted (demand) distributions up to any period in the planning interval. A further contribution of this paper is an (accuracy) improvement heuristic, called fine-tuning, executed once the fix-and-optimize (FO) heuristic to solve a scenario-based mixed integer programming model has been completed. Fine-tuning uses linear programming (LP) with fixed binary variables (e.g., setup decisions) generated by FO and iteratively adapts production quantities so that compliance with given expected service level constraints is reached. The LP is solved with relatively little computational effort, even for large(r) sets of scenarios. We show the advancements possible with MPDS and fine-tuning by solving numerous test instances of the stochastic capacitated lot-sizing problem under a static uncertainty approach. [ABSTRACT FROM AUTHOR]

Two-sample location-scale refers to a model that permits a pair of standardised random variables to have a common base distribution. Function-based hypothesis testing in these models refers to formal tests based on distributions functions, or direct transformations thereof, that would help decide whether or not two samples come from some location-scale family of distributions. For uncensored data, an approach of testing based on plug-in empirical likelihood (PEL) is carried out with sample means and standard deviations as the plug-ins. The method extends to censored data, where censoring adjusted moment estimators provide the requisite plug-ins. The large sample null distribution of the PEL statistic is derived. Since it is not distribution free, a two-sample location-scale appropriate resampling is employed to obtain thresholds needed for the testing. Numerical studies are carried out to investigate the performance of the proposed method. Real examples are presented for both the uncensored and censored cases. [ABSTRACT FROM AUTHOR]

Motivated by risk measure, super-hedge pricing, and modeling uncertainty in finance, Shige Peng established the theory of sub-linear expectation. In this article, we derive two results of laws of large numbers in the framework of sub-linear expectations. One is the strong law of large numbers for the array of random variables, which satisfies non identical distributed and exponential negatively dependent under sub-linear expectation. The other is the weak law of large numbers for the array of random variables, which satisfies non identical distributed and Φ -negatively dependent under sub-linear expectation. These results include and extend some existing results. [ABSTRACT FROM AUTHOR]

This study reports results from a stochastic techno-economic analysis (TEA) model that assessed the financial feasibility of forest biomass harvest for low-carbon bioenergy feedstocks in the hardwood region of the Northeast United States. It analyzed three 24-year scenarios based on primary data collected from the mixed product harvest with whole tree harvesting systems that primarily produce clean chips, dirty chips, or pulpwood and dirty chips. Using a joint product costing approach, proportional costs of shared processes were allocated to different products on a mass basis. Uncertainty associated with key stochastic variables was incorporated into the model to generate net present values (NPV), benefit–cost ratios (BCR), and minimum selling prices (MSP) via Monte Carlo simulation. The clean chip scenario produced an NPV of $1.36 million and a BCR of 1.03, while the pulpwood scenario's NPV and BCR ($0.06 million and 1.02) were lower, and the dirty chip scenario generated negative NPV (− $0.02 million) and a BCR of 0.99. The probabilities of achieving positive NPVs for all three scenarios fell between 47 and 56%. The mean MSP for one clean chip scenario was $94.03/dry Mg, while the mean MSPs for two dirty chip scenarios were $74.79/dry Mg and $75.93/dry Mg. NPV results were most sensitive to forest biomass feedstock harvesting production levels, transportation distances, and delivered prices, followed by diesel fuel consumption for in-wood harvest and diesel fuel price. [ABSTRACT FROM AUTHOR]

In system reliability, coherent systems play a central role since without them any system is considered flawed. A system is coherent if all the components are relevant to that system i.e. functioning of every component has an effect in the functioning of the system and the structure of the system is monotone. Monotone structure means that improving any component will not deteriorate the system. A mixed system is a stochastic mixture of coherent systems and any coherent system is a special case of a mixed system. In reliability engineering, one major problem is to compare various coherent and mixed systems so that the better system can be used to increase the overall reliability. Another important problem is to measure the complexity of systems. A highly complex system will naturally have a higher running and maintenance cost associated with it and it is desirable for a reliability engineer to have an understanding regarding the complexity of systems beforehand. In this paper, we address these two problems from an information theoretic approach. Extropy is a measure of information which is the dual of the famous Shannon entropy measure. Recently, a new measure related to extropy, called cumulative residual extropy (CREx), was introduced in the literature by Jahanshahi et al. (Probab Eng Inf Sci 1–21, 2019). This measure is based on the survival function of the underlying random variable and it has some advantages over extropy measure. In this work, we analyze the CREx measure for coherent and mixed systems and develop some comparison results among systems. We also obtain some bounds of CREx of coherent and mixed systems consisting of independent and identically distributed (iid) and dependent and identically distributed (d.i.d.) components. We propose a new divergence measure to calculate the complexity of systems having iid components. Also, we introduced a new discrimination measure to compare various coherent and mixed systems when pairwise comparisons by usual stochastic order is not possible. Finally, we discuss analysis of the CREx measure of coherent systems having heterogeneous components. We also provide applications involving redundancy allocation. Various numerical examples are considered for illustrative purposes. [ABSTRACT FROM AUTHOR]

In highly-competitive markets, product quality is a critical element of sustainable development for manufacturing enterprises. The pursuit of quality is in essence a commitment to meeting the needs and expectations of customers. Firms often express customer needs in terms of quality characteristics in order to evaluate, monitor, and improve process performance. Reliability is an important quality characteristic. Specifically, reliability is the probability that a product will function as intended and will not malfunction within a certain period of time under certain operating conditions. Clearly, reliability influences the final evaluation made by customers of product quality. Since reliability is a time-oriented quality characteristic, it follows an exponential distribution. The performance standard for most quality indices is 1. To bring evaluation of reliability in line with convention, we propose ratio-based lifetime performance index (RLPI) θ L . However, time-oriented data are continuous random variables, which implies that the observed values of the data are not precise. Furthermore, the performance of a product in various aspects inevitably declines over time. Clearly, longer product lifetime is not always better; it depends on the type of product. We therefore propose a two-tailed fuzzy statistical test for the RLPI θ L to assist manufacturing enterprises in making more accurate evaluations of product reliability. An illustrative example is presented to demonstrate the practical applicability of our proposed approach. [ABSTRACT FROM AUTHOR]

We study a geometric version of first-passage percolation on the complete graph, known as long-range first-passage percolation. Here, the vertices of the complete graph K n are embedded in the d-dimensional torus T n d , and each edge e is assigned an independent transmission time T e = ‖ e ‖ T n d α E e , where E e is a rate-one exponential random variable associated with the edge e, ‖ · ‖ T n d denotes the torus-norm, and α ≥ 0 is a parameter. We are interested in the case α ∈ [ 0 , d) , which corresponds to the instantaneous percolation regime for long-range first-passage percolation on Z d studied by Chatterjee and Dey [14], and which extends first-passage percolation on the complete graph (the α = 0 case) studied by Janson [24]. We consider the typical distance, flooding time, and diameter of the model. Our results show a 1, 2, 3-type result, akin to first-passage percolation on the complete graph as shown by Janson. The results also provide a quantitative perspective to the qualitative results observed by Chatterjee and Dey on Z d . [ABSTRACT FROM AUTHOR]

This paper examines nonlinear and time‐varying dependence structures between a pair of stochastic variables, using a novel approach which combines regime‐switching models and local Gaussian correlation (LGC). We propose an LGC‐based bootstrap test for examining whether the dependence structure between two variables is equal across different regimes. We examine this test in a Monte Carlo study, where it shows good level and power properties. We argue that this approach is more intuitive than competing approaches, typically combining regime‐switching models with copula theory. Furthermore, LGC is a semi‐parametric approach, hence avoids any parametric specification of the dependence structure. We illustrate our approach using financial returns from the US–UK stock markets and the US stock and government bond markets, and provide detailed insight into their dependence structures. [ABSTRACT FROM AUTHOR]

A metric tensor for Riemann manifold Monte Carlo particularly suited for nonlinear Bayesian hierarchical models is proposed. The metric tensor is built from symmetric positive semidefinite log‐density gradient covariance (LGC) matrices, which are also proposed and further explored here. The LGCs generalize the Fisher information matrix by measuring the joint information content and dependence structure of both a random variable and the parameters of said variable. Consequently, positive definite Fisher/LGC‐based metric tensors may be constructed not only from the observation likelihoods as is current practice, but also from arbitrarily complicated nonlinear prior/latent variable structures, provided the LGC may be derived for each conditional distribution used to construct said structures. The proposed methodology is highly automatic and allows for exploitation of any sparsity associated with the model in question. When implemented in conjunction with a Riemann manifold variant of the recently proposed numerical generalized randomized Hamiltonian Monte Carlo processes, the proposed methodology is highly competitive, in particular for the more challenging target distributions associated with Bayesian hierarchical models. [ABSTRACT FROM AUTHOR]

The main concern is the uncertainty in the real-world solid transportation problem. This study examines a supply, demand, and conveyance capacity-based multi-choice solid stochastic multi-objective transportation problem (MCSS-MOTP). Due to uncertainty, the concrete objective function coefficients of the proposed model are of multivariate type. Furthermore, the parameters of the constraints are treated as independent multivariate random variables with normal distribution. First, a Newton divided difference method-based interpolation polynomial is described that extends an interpolation polynomial using practical properties at non-negative integer nodes to deal with any multiple-choice parameter. Second, the probabilistic constraints are converted into precise ones utilizing a stochastic programming approach. In the end, ranking procedure was used to compare the existing approach with the old models. The proposed model’s applicability was confirmed using a numerical example. [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]

Let {Xυ: υ ∈ ℤd} be i.i.d. random variables. Let S (π) = ∑ υ ∈ π X υ be the weight of a self-avoiding lattice path π. Let M n = max { S (π) : π has length n and starts from origin }. We are interested in the asymptotics of Mn as n → ∞. This model is closely related to the first passage percolation when the weights {Xυ: υ ∈ ℤd} are non-positive and it is closely related to the last passage percolation when the weights {Xυ, υ ∈ ℤd} are non-negative. For general weights, this model could be viewed as an interpolation between first passage models and last passage models. Besides, this model is also closely related to a variant of the position of right-most particles of branching random walks. Under the two assumptions that ∃ α > 0 , E (X 0 +) d (log + X 0 +) d + α < + ∞ and that E [ X 0 − ] < + ∞ , we prove that there exists a finite real number M such that Mn/n converges to a deterministic constant M in L1 as n tends to infinity. And under the stronger assumptions that ∃ α > 0 , E (X 0 +) d (log + X 0 +) d + α < + ∞ and that E [ (X 0 −) 4 ] < + ∞ , we prove that Mn/n converges to the same constant M almost surely as n tends to infinity. [ABSTRACT FROM AUTHOR]

Bivariate extreme value distributions can be used to model dependence of observations from random variables in extreme levels. There is no finite dimensional parametric family for these distributions, but they can be characterized by a certain one-dimensional function which is known as Pickands dependence function. In many applications the general approach is to estimate the dependence function with a non-parametric method and then conduct further analysis based on the estimate. Although this approach is flexible in the sense that it does not impose any special structure on the dependence function, its main drawback is that the estimate is not available in a closed form. This paper provides some theoretical results which can be used to find a closed form approximation for an exact or an estimate of a twice differentiable dependence function and its derivatives. We demonstrate the methodology by calculating approximations for symmetric and asymmetric logistic dependence functions and their second derivatives. We show that the theory can be even applied to approximating a non-parametric estimate of dependence function using a convex optimization algorithm. Other discussed applications include a procedure for testing whether an estimate of dependence function can be assumed to be symmetric and estimation of the concordance measures of a bivariate extreme value distribution. Finally, an Australian annual maximum temperature dataset is used to illustrate how the theory can be used to build semi-infinite and compact predictions regions. [ABSTRACT FROM AUTHOR]

For 0<λ<1$$ 0<\lambda <1 $$ and n→∞$$ n\to \infty $$ pick uniformly at random λn$$ \lambda n $$ vectors in {0,1} n$$ {\left\{0,1\right\}}^n $$ and let C$$ C $$ be the orthogonal complement of their span. Given 0<γ<12$$ 0<\gamma <\frac{1}{2} $$ with 0<λ

We revisit a deterministic model for studying the dynamics of allelopathy. The model is formulated in terms of a non-homogeneous linear system of differential equations whose forcing or source term is a piecewise constant function (square wave). To account for the inherent uncertainties present in this natural phenomenon, we reformulate the model as a system of random differential equations where all model parameters and the initial condition are assumed to be random variables, while the forcing term is a stochastic process. Taking extensive advantage of the so-called Random Variable Transformation (RVT) method, we obtain the solution of the randomized model by providing explicit expressions of the first probability density function of the solution under very general assumptions on the model data. We also determine the joint probability density function of the non-trivial equilibrium point, which is a random vector. If the source term is a time-dependent stochastic process, the RVT method might not be applicable since no explicit solution of the model is available. We then show an alternative approach to overcome this drawback by applying the Liouville–Gibbs partial differential equation. All the theoretical findings are illustrated through several examples, including the application of the randomized model to real-world data on alkaloid contents from leaching thornapple seed. [ABSTRACT FROM AUTHOR]

The evidence of soil nonuniformity has been reported in several site investigation reports and is well-confirmed for any soil in general. However, studies related to the spatial soil variability of offshore ground are somewhat limited, and current design practices for monopile foundations also overlook the uncertainty of the offshore ground. This paper presents the probabilistic evaluation of the serviceability limit state of monopile foundations considering the spatial variability of offshore ground. The nonuniformity of the ground is modeled utilizing the site-specific undrained shear strength (su) as a stochastic variable, using a spatially correlated Gaussian random field. A hardening soil constitutive model is utilized in 3D finite element analysis of offshore ground, with a focus on parameter calibration. The reliability of the serviceability limit state is assessed based on the allowable load on the pile head. The stochastic behavior of the maximum bending moment and maximum shear force along the depth of the monopile is also investigated. Besides, the paper also highlights the importance of incorporating ground nonuniformity during the design process of a monopile foundation. [ABSTRACT FROM AUTHOR]

The team orienteering problem (TOP) is an NP‐hard optimization problem with an increasing number of potential applications in smart cities, humanitarian logistics, wildfire surveillance, etc. In the TOP, a fixed fleet of vehicles is employed to obtain rewards by visiting nodes in a network. All vehicles share common origin and destination locations. Since each vehicle has a limitation in time or traveling distance, not all nodes in the network can be visited. Hence, the goal is focused on the maximization of the collected reward, taking into account the aforementioned constraints. Most of the existing literature on the TOP focuses on its deterministic version, where rewards and travel times are assumed to be predefined values. This paper focuses on a more realistic TOP version, where travel times are modeled as random variables, which introduces reliability issues in the solutions due to the route‐length constraint. In order to deal with these complexities, we propose a simheuristic algorithm that hybridizes biased‐randomized heuristics with a variable neighborhood search and MCS. To test the quality of the solutions generated by the proposed simheuristic approach, we employ the well‐known sample average approximation (SAA) method, as well as a combination model that hybridizes the metaheuristic used in the simheuristic approach with the SAA algorithm. The results show that our proposed simheuristic outperforms the SAA and the hybrid model both on the objective function values and computational time. [ABSTRACT FROM AUTHOR]

AbstractIn the context of actuarial science, the second largest claim amount is crucial to insurance analysis since they provide useful information for determining annual premium. In this article, we provide sufficient conditions of the second largest claim amounts arising from two sets of dependent and heterogeneous individual risk models according to various stochastic orders. It is first shown that the reversed hazard order between the occurrence probabilities vectors implies the reversed hazard order of the second largest claim amounts under certain conditions. Second, sufficient conditions are established for the usual stochastic ordering of the second largest claim amounts arising from heterogeneous dependent individual risk models under copula dependence. Finally, several examples illustrating the theoretical results are presented as well. [ABSTRACT FROM AUTHOR]

AbstractLet us consider a sequence of binary (zero-one) trials. A counter registers ones but once an one is registered the mechanism is locked for a fixed number of trials following each registration. On such a sequence of a fixed length we define a random variable enumerating runs of ones of length exceeding a threshold. Exact recursive expressions are obtained for the probability mass function, generating functions and moments, as well as an exact closed formula for the mean of this random variable. A simulation algorithm is also provided for approximating values of this random variable on such a modified binary sequence. Statistical inference problems associated with the probability of ones are examined by numerical techniques and simulation. An application connected to the chance that a stochastic process remains or not in statistical control is discussed. Illustrative numerical examples exemplify further the theoretical results. [ABSTRACT FROM AUTHOR]

This year is the 50th anniversary of Besag's classic auto‐models publication, a cornerstone in the development of modern‐day spatial statistics/econometrics. Besag struggled for nearly two decades to make his conceptualization collectively successful across a wide suite of random variables. But only his auto‐normal, and to a lesser degree his auto‐logistic/binomial, were workable. Others, like his auto‐Poisson, were effectively failures, whereas still others, such as potentials like an auto‐Weibull, defied even awkward mathematical incorporations of spatial lag terms. Besag circumvented this impediment by introducing an auto‐normal random effects components (within a Bayesian estimation context), building upon his single total success. This article describes an alternative approach, partly paralleling his reformulation while avoiding inserting spatial lag terms directly into probability density/mass functions, implanting spatial autocorrelation into cumulative distributions functions (CDFs), instead, via a spatially autocorrelated uniform distribution. The already existing probability integral transform and quantile function mathematical statistics theorems enable this mechanism to spatialize any random variable, with these new ones labeled sui‐models. [ABSTRACT FROM AUTHOR]

In this paper, we demonstrate the Anderson localization effect in coupled metamaterial structures. We introduce the random variables by randomly choosing the geometrical parameter of structures and randomly choosing the distance between structures to reduce the coupling of metamaterial and this decoupling effect is equivalent to Anderson localization effect, which can reduce the coupling without enlarging the area of unit cell. We demonstrate our idea by employing the experiments. Furthermore, we present an example of deflector to see how this decoupling effect can help us design functional devices. [ABSTRACT FROM AUTHOR]

AbstractThe hyperbolic secant distribution has several generalizations with applications in, for example, finance. In this study, we explore the dual geometric structure of one such generalization: the beta-logistic distribution. Within this family, two special cases of random variables, as examples, are of particular interests: their moments, by some recent results, give the Bernoulli and Euler polynomials, which are important objects in many areas of mathematics. This current study also uncovers that the beta-logistic distribution admits a α-parallel prior for any real number α, that has the potential for application in geometric statistical inference. [ABSTRACT FROM AUTHOR]

Introduction: Since their identification in 1974, circoviruses have caused clinicopathological diseases in various animal species, including humans. However, their origin, transmission, and genetic evolution remain poorly understood. Methods: In this study, the genome sequences of circovirus were obtained from GenBank, and the Bayesian stochastic search variable selection algorithm was employed to analyzed the evolution and origin of circovirus. Results: Here, the evolutionary origin, mode of transmission, and genetic recombination of the circovirus were determined based on the available circovirus genome sequences. The origin of circoviruses can be traced back to fish circovirus, which might derive from fish genome, and human contributes to transmission of fish circovirus to other species. Furthermore, mosquitos, ticks, bats, and/or rodents might play a role as intermediate hosts in circovirus intraand inter-species transmission. Two major lineages (A and B) of circoviruses are identified, and frequent recombination events accelerate their variation and spread. The time to the most recent common ancestor of circoviruses can be traced back to around A.D. 600 and has been evolving at a rate of 10-4 substitutions site-1 year-1 for a long time. Discussion: These comprehensive findings shed light on the evolutionary origin, population dynamics, transmission model, and genetic recombination of the circovirus providing valuable insights for the development of prevention and control strategies against circovirus infections. [ABSTRACT FROM AUTHOR]

In this article, we consider the weighted least squares estimators (WLSEs) of the unknown parameters of a multiple sinusoidal model. Although, the least squares estimators (LSEs) are known to be the most efficient estimators in case of a multiple sinusoidal model, they are quite susceptible in presence of outliers. In presence of outliers, robust estimators like the least absolute deviation estimators (LADEs) or Huber's M-estimators (HMEs) may be used. But implementation of the LADEs and HMEs are quite challenging in case of a sinusoidal model, the problem becomes more severe in case of multiple sinusoidal model. Moreover, to derive the theoretical properties of the robust estimators, one needs stronger assumptions on the error random variables than what are needed for the LSEs. The proposed WLSEs are used as robust estimators and they have the following two major advantages. First, they can be implemented very easily in case of multiple sinusoidal model, and their properties can be obtained under the same set of error assumptions as the LSEs. Extensive simulation results suggest that in presence of outliers, the WLSEs behave better than the LSEs, and at par with the LADEs and HEMs. It is observed that the performance of the WLSEs depend on the weight function, and we discuss how to choose a proper weight function for a given data set. We have analyzed one synthetic data set to show how the proposed methods can be implemented in practice. [ABSTRACT FROM AUTHOR]

A network evolution with predicted tail and extremal indices of PageRank and the Max-Linear Model used as node influence indices in random graphs is considered. The tail index shows a heaviness of the distribution tail. The extremal index is a measure of clustering (or local dependence) of the stochastic process. The cluster implies a set of consecutive exceedances of the process over a sufficiently high threshold. Our recent results concerning sums and maxima of non-stationary random length sequences of regularly varying random variables are extended to random graphs. Starting with a set of connected stationary seed communities as a hot spot and ranking them with regard to their tail indices, the tail and extremal indices of new nodes that are appended to the network may be determined. This procedure allows us to predict a temporal network evolution in terms of tail and extremal indices. The extremal index determines limiting distributions of a maximum of the PageRank and the Max-Linear Model of newly attached nodes. The exposition is provided by algorithms and examples. To validate our theoretical results, our simulation and real data study concerning a linear preferential attachment as a tool for network growth are provided. [ABSTRACT FROM AUTHOR]

This paper aims at assessing the failure time of a 7‐story reinforced concrete (RC) frame in a post‐earthquake fire (PEF) event probabilistically. Cumulative distribution functions (CDF) of the studied frame's failure time in various seismic load intensities have been calculated and presented with the aid of Monte Carlo analysis. Seismic load intensity, failure time, and failure probability are three parameters that are correlated through probabilistic analysis. The effects of cracking, spalling, and residual deformations resulted from the seismic load are considered in the strength of structure against the fire load. Seismic load intensity, materials properties, gravity load, and geometry are considered as random variables and one probabilistic analysis has been carried out for each seismic load intensity. The results have illustrated that in low seismic load intensities, probabilistic values of failure time in a structure subjected to pure fire load are equal to the one exposed to PEF. With the increase of seismic load intensity, the effects of cracking, spalling, and residual deformations would lead to a decline in the strength of structural elements against PEF scenario. The failure time in 50% failure probability for Sa = 0.2 g, Sa = 1 g, and Sa = 2 g intensities has been calculated as 14,300, 12,200, and 5100 s, respectively. The analysis results have shown that in an unspecified seismic load intensity, the failure time of the 7‐story RC frame for the 50% occurrence probability is equal to 9750 s. [ABSTRACT FROM AUTHOR]

A robust trajectory planning method for non-cooperative target rendezvous is investigated based on closed-loop uncertainty analysis. The proposed method addresses the issue that uncertainties affect the optimality of objective functions and the reliability of constraints. Considering multiple uncertainties, a stochastic optimal rendezvous model with a robustness performance index and chance constraints is presented with line-of-sight dynamics. The guidance model, angles-only navigation model and control model are derived, and uncertainty propagation equations for closed-loop GN & C system is proposed by using linear covariance analysis. The stochastic optimal rendezvous model is transformed into a robust optimal rendezvous model by using 3- σ of the random variables. The genetic algorithm is used to solve the robust trajectory planning problem, and a series of examples demonstrate that the robust maneuver solution can be significantly better than the solution corresponding to deterministic trajectory optimization problem. [ABSTRACT FROM AUTHOR]

Let X$X$ be a random variable and define its concentration function by Qh(X)=supx∈RP(X∈(x,x+h]).$$\begin{equation*} {\mathcal {Q}}_{h}(X)=\sup _{x\in {\mathbb {R}}}{\mathbb {P}}(X\in (x,x+h]). \end{equation*}$$For a sum Sn=X1+⋯+Xn$S_n=X_1+\cdots +X_n$ of independent real‐valued random variables, the Kolmogorov–Rogozin inequality states that Qh(Sn)⩽C∑i=1n(1−Qh(Xi))−12.$$\begin{equation*} {\mathcal {Q}}_{h}(S_n)\leqslant C{\left(\sum _{i=1}^{n}(1-{\mathcal {Q}}_{h}(X_i))\right)}^{-\frac{1}{2}}. \end{equation*}$$In this paper, we give an optimal bound for Qh(Sn)${\mathcal {Q}}_{h}(S_n)$ in terms of Qh(Xi)${\mathcal {Q}}_{h}(X_i)$, which settles a question posed by Leader and Radcliffe in 1994. Moreover, we show that the extremal distributions are mixtures of two uniform distributions each lying on an arithmetic progression. [ABSTRACT FROM AUTHOR]

Abstract.In this article, by means of Rosenthal-type inequality, we study the complete convergence and strong law of large numbers for weighted sums of m-widely accpetable random variables under sub-linear expectations, which extend some existing results in classical probability space. As applications, we investigate the complete consistency and strong consistency of weighted estimators in nonparametric regression models under sub-linear expectations. In addition, we provide some simulation studies to verify the finite sample performance of the theoretical results. [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: Autism spectrum conditions (ASC) and quantitative autistic traits (QATs) are associated with sensory symptoms, which may contribute to anxiety and adversely affect social and cognitive development. Although sensory symptoms can occur across all senses, the relative roles of specific sensory modalities as contributors to the autistic phenotype and to anxiety are not well understood. The objective of this study was to examine which sensory symptoms were most predictive of high anxiety. Methods: We recruited 257 female primary caregivers of children aged 6 to 11 years (49% girls) to a questionnaire study comprising parent-report measures for classical QATs (social, communicative, and rigid), autism-related sensorimotor symptoms (visual, auditory, tactile, olfactory, gustatory, vestibular, proprioceptive, and motor), and anxiety symptoms. First, Bayesian stochastic search variable selection (SSVS) was used to identify the most probable sensorimotor predictors of specific QATs as well as diagnosed ASC. Then, the selected predictors were used in another SSVS, using anxiety symptoms as a dependent variable, to identify which of the autism-relevant sensorimotor symptoms were most robustly predictive of anxiety. Finally, the effect sizes of anxiety-related sensory symptoms were estimated with linear regressions. Results: We found that auditory symptoms and motor difficulties were most predictive of ASC diagnosis. Developmental motor difficulties were also strongly related to all individual QATs, whereas auditory symptoms were more selectively predictive of rigid traits. Tactile symptoms robustly predicted social interaction QATs, and proprioceptive symptoms predicted communicative QATs. Anxiety outcomes were most strongly predicted by difficulties with auditory and olfactory processing. Conclusions: The results support the clinical importance of being alert to complaints about sounds and hearing in neurodevelopmental populations, and that auditory processing difficulties may be evaluated as an early marker of poor mental health in children with and without diagnosed autism. Olfactory processing differences appeared to be an anxiety marker less strongly associated with ASC or QATs, while motor difficulties were highly autism-relevant but not equally strongly associated with anxiety outcomes. We suggest that future studies may focus on the mechanisms and consequences of neurodevelopmental central auditory processing dysfunction and its potential relationship to anxiety disorders. [ABSTRACT FROM AUTHOR]

Correlation coefficients and linear regression values computed from group averages can differ from correlation coefficients and linear regression values computed using individual scores. This observation known as the ecological fallacy often assumes that all the individual scores are available from a population. In many situations, one must use a sample from the larger population. In such cases, the computed correlation coefficient and linear regression values will depend on the sample that is chosen and the underlying sampling distribution. The sampling distribution of correlation coefficients and linear regression values for group averages will be identical to the sampling distribution for individuals for normally distributed variables for random samples drawn from infinitely large continuous distributions. However, data that is acquired in practice is often acquired when sampling without replacement from a finite population. Our objective is to demonstrate through Monte Carlo simulations that the sampling distributions for correlation and linear regression will also be similar for individuals and group averages when sampling without replacement from normally distributed variables. These simulations suggest that when a random sample from a population is selected, the correlation coefficients and linear regression values computed from individual scores will not be more accurate in estimating the entire population values compared to samples when group averages are used as long as the sample size is the same. [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]

AbstractObtaining probabilistic models is of high relevance in many recent applications. However, estimation of such distributional models with very large datasets remains a difficult task. In particular, the use of rather complex models can easily lead to memory-related efficiency problems and thereby make estimation infeasible even on high-performance computers. We address these challenges and propose a novel backfitting algorithm, which is based on the ideas of stochastic gradient descent and can deal virtually with any amount of data on a conventional laptop. The algorithm performs automatic selection of variables and determination of smoothing parameters. Its performance is superior or at least equivalent to other implementations for structured additive distributional regression, such as, gradient boosting, while maintaining lower computation time. Performance is evaluated using an extensive simulation study and an exceptionally challenging example of lightning count prediction across Austria with over 9 million observations and 80 covariates. [ABSTRACT FROM AUTHOR]

When assessing the reliability of a system or the viability of a material, it is necessary to consider the stress conditions of the operating system. Let X be the strength of the system and Y be the stress of the system caused by the environment. In a stress–strength model, the system’s reliability is defined as P(X>Y), and due to ignoring environmental shocks or human failure, it is usually overestimated. To underestimate reliability, we assume that when X goes to the environmental conditions, the system’s strength reduces to ZX, where Z is a random variable on (0,1). We propose a modified reliability model with Ru=P(ZX>Y) for the gamma distribution. In this model, stress Y and the scale mixture of the strength of the gamma distribution, ZX, are modeled as independent random variables. The proposed model is compared with the traditional model through a simulation study. Additionally, the asymptotic distribution is used to construct an asymptotic confidence interval for Ru. Finally, we use two real datasets to demonstrate the practical applicability of our proposed method. [ABSTRACT FROM AUTHOR]

AbstractRecently, a measure of uncertainty termed by negative cumulative extropy (NCEX) is proposed by Tahmasebi and Toomaj (2022). It is a flexible extension of extropy measure which was proposed by Lad, Sanfilippo, and Agro (2015). To measure the uncertainty of uncertain variables, in this article, we propose the concept of NCEX through uncertainty distributions. Some properties of NCEX are derived, and some practical examples of uncertain variables are given. Several basic theorems are proposed. A formula of cross-extropy is defined via inverse uncertainty distributions. We also delve into a pattern recognition problem to highlight the importance of cross-extropy. Finally, applications to portfolio selection and signal processing are presented. [ABSTRACT FROM AUTHOR]

Abstract–Posterior computation in hierarchical Dirichlet process (HDP) mixture models is an active area of research in nonparametric Bayes inference of grouped data. Existing literature almost exclusively focuses on the Chinese restaurant franchise (CRF) analogy of the marginal distribution of the parameters, which can mix poorly and has a quadratic complexity with the sample size. A recently developed slice sampler allows for efficient blocked updates of the parameters, but is shown to be statistically unstable in our article. We develop a blocked Gibbs sampler that employs a truncated approximation of the underlying random measures to sample from the posterior distribution of HDP, which produces statistically stable results, is highly scalable with respect to sample size, and is shown to have good mixing. The heart of the construction is to endow the shared concentration parameter with an appropriately chosen gamma prior that allows us to break the dependence of the shared mixing proportions and permits independent updates of certain log-concave random variables in a block. En route, we develop an efficient rejection sampler for these random variables leveraging piece-wise tangent-line approximations. Supplementary materials, which include substantive additional details and code, are available online. [ABSTRACT FROM AUTHOR]

AbstractThis paper proposes a new association statistic for determining whether random variables are statistically independent. The proposed association statistic can also be used to examine the strength of both linear and non-linear dependency between variables. This statistic is derived by examining how the conditional probabilities of events differ from their corresponding marginal probabilities. The new statistic is defined in terms of the probability of acceptance commonly associated with the Accept-Reject algorithm and has a very simple formula. The simulated density of the probability of acceptance can be used to measure the degree of uncertainty of the estimated values of the new association statistic. The results from simulations as well as examples that employ real data indicate that this new association statistic is very powerful in detecting linear and non-linear associations between two random variables. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR]