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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 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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

AbstractThe marketing authorization of a medicinal product is contingent upon demonstration of safety and efficacy in support of the product’s labeled conditions of use. To demonstrate safety, one group of adverse events that requires detailed consideration is common adverse reactions (ARs). ARs and their frequency are reported in prescription drug labeling in the US and EU. The determination of these adverse reactions generally takes a simple approach - usually, inclusion is through the frequency of reporting and whether the adverse event (AE) rate for the drug exceeds the placebo rate. This standard method does not account for confounders or multiplicity. To overcome these limitations, we propose a Monte-Carlo approach to detect drug safety signals in clinical trials. We fit regression models incorporating covariates to assess the drug effect on the rate of AEs. Adjustment for multiplicity is carried out through the construction of simultaneous confidence intervals accounting for arbitrary correlations. A computationally efficient multiplier bootstrap approach using the Rademacher sequences is developed to generate random samples from the joint distribution of the estimators for all the AE rates. Compared to Bonferroni-based methods, the proposed method leads to narrower simultaneous confidence intervals and is more powerful in detecting potential safety signals. [ABSTRACT FROM AUTHOR]

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

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

We propose a novel extremal dependence measure called the partial tail-correlation coefficient (PTCC), in analogy to the partial correlation coefficient in classical multivariate analysis. The construction of our new coefficient is based on the framework of multivariate regular variation and transformed-linear algebra operations. We show how this coefficient allows identifying pairs of variables that have partially uncorrelated tails given some other variables in a random vector. Unlike other recently introduced conditional independence frameworks for extremes, our approach requires minimal modeling assumptions and can thus be used in exploratory analyses to learn the structure of extremal graphical models. Similarly to traditional Gaussian graphical models where edges correspond to the nonzero entries of the precision matrix, we can exploit classical inference methods for high-dimensional data, such as the graphical Lasso with Laplacian spectral constraints, to efficiently learn the extremal network structure via the PTCC. We apply our new method to study extreme risk networks in two different datasets (extreme river discharges and historical global currency exchange data) and show that we can extract interesting extremal structures with meaningful domain-specific interpretations. [ABSTRACT FROM AUTHOR]

The Lindley distribution is useful in a wide variety of fields, such as biology and astronomy. Many generalizations of the Lindley distribution have been introduced in the literature, with various motivations. Inspired by the concept of superstatistics in nonequilibrium statistical mechanics, we introduce here a novel generalization of the Lindley distribution, by regarding its shape parameter as a stochastic variable. This procedure is particularly well motivated in astronomy applications, since this parameter may fluctuate over a large spatiotemporal scale. By appealing to the central limit theorem, two families of distributions are constructed, associated with additive and multiplicative random processes. We discuss in detail these distributions, we study their asymptotic behavior, and compute their moments. We briefly discuss their possible use in astronomy, biology, and elsewhere. [ABSTRACT FROM AUTHOR]

AbstractThis article is concerned with the local linear non parametric regression estimator of a right censored scalar response random variable, given a functional random covariate. First, we investigate its asymptotic normality under the concentration properties of small ball probability functions. Then, we apply the results to present the asymptotic (1−α) confidence interval of the regression function for 0<α<1. To lend further support to our theoretical results, we carry out a simulation study to illustrate the performance and the asymptotic Gaussian behavior of our estimator. Finally, an application to real data is provided. [ABSTRACT FROM AUTHOR]

Reliability analysis of the complex structural system is a popular issue due to complex failure regions and frequently time-consuming simulations. In this work, a new method based on the active learning Kriging model is proposed to solve the problem with both random and interval hybrid uncertainty. The proposed method divides the original variable space based on the proposed adaptive important exploration region (AIER), which approximates only the bounds of the failure domain. In each iteration, the proposed approach selects the optimal training point from the AIER by utilizing a predicted sign error function related to the system indicator function, which can effectively measure the uncertainty of the complex system. Subsequently, the error estimation of the failure probability is used as the convergence criterion to ensure the accuracy and efficiency of reliability analysis. Afterward, the performance of the proposed method is evaluated by investigating four examples, which show the reasonability and superiority of this method. Finally, the multibody dynamics simulation of the flap mechanism is presented, which involves the aerodynamic load analysis and the simulation modeling. Considering the two failure modes of stuck and insufficient accuracy, it is shown that the proposed method greatly reduces the number of calls for the simulation model and ensures the accuracy of the evaluation during the reliability analysis of the flap mechanism. [ABSTRACT FROM AUTHOR]

We consider the Gaussian interface model in the presence of random external fields, that is the finite volume (random) Gibbs measure on R Λ N , Λ N = [ - N , N ] d ∩ Z d with Hamiltonian H N (ϕ) = 1 4 d ∑ x ∼ y (ϕ (x) - ϕ (y)) 2 - ∑ x ∈ Λ N η (x) ϕ (x) and 0-boundary conditions. { η (x) } x ∈ Z d is a family of i.i.d. symmetric random variables. We study how the typical maximal height of a random interface is modified by the addition of quenched bulk disorder. We show that the asymptotic behavior of the maximum changes depending on the tail behavior of the random variable η (x) when d ≥ 5 . In particular, we identify the leading order asymptotics of the maximum. [ABSTRACT FROM AUTHOR]

Background: Most stroke patients suffer from an imbalance in blood supply, which causes severe brain damage leading to functional deficits in motor, sensory, swallowing, cognitive, emotional, and speech functions. Repetitive transcranial magnetic stimulation (rTMS) is thought to restore functions impaired during the stroke process and improve the quality of life of stroke patients. However, the efficacy of rTMS in treating post-stroke function impairment varies significantly. Therefore, we conducted a meta-analysis of the number of patients with effective rTMS in treating post-stroke dysfunction. Methods: The PubMed, Embase, and Cochrane Library databases were searched. Screening and full-text review were performed by three investigators. Single-group rate meta-analysis was performed on the extracted data using a random variable model. Then subgroup analyses were performed at the levels of stroke acuity (acute, chronic, or subacute); post-stroke symptoms (including upper and lower limb motor function, dysphagia, depression, aphasia); rTMS stimulation site (affected side, unaffected side); and whether or not it was a combination therapy. Results: We obtained 8955 search records, and finally 33 studies (2682 patients) were included in the meta-analysis. The overall analysis found that effective strength (ES) of rTMS was 0.53. In addition, we found that the ES of rTMS from acute/subacute/chronic post-stroke was 0.69, 0.45, and 0.52. We also found that the ES of rTMS using high-frequency stimulation was 0.56, while the ES of rTMS using low-frequency stimulation was 0.53. From post-stroke symptoms, we found that the ES of rTMS in sensory aspects, upper limb functional aspects, swallowing function, and aphasia was 0.50, 0.52, 0.51, and 0.54. And from the site of rTMS stimulation, we found that the ES of rTMS applied to the affected side was 0.51, while the ES applied to the unaffected side was 0.54. What's more, we found that the ES of rTMS applied alone was 0.53, while the ES of rTMS applied in conjunction with other therapeutic modalities was 0.53. Conclusions: By comparing the results of the data, we recommend rTMS as a treatment option for rehabilitation of functional impairment in patients after stroke. We also recommend that rehabilitation physicians or clinicians use combination therapy as one of the options for patients. [ABSTRACT FROM AUTHOR]

We study the response of a quantitative trait to exponential directional selection in a finite haploid population, both at the genetic and the phenotypic level. We assume an infinite sites model, in which the number of new mutations per generation in the population follows a Poisson distribution (with mean Θ) and each mutation occurs at a new, previously monomorphic site. Mutation effects are beneficial and drawn from a distribution. Sites are unlinked and contribute additively to the trait. Assuming that selection is stronger than random genetic drift, we model the initial phase of the dynamics by a supercritical Galton–Watson process. This enables us to obtain time-dependent results. We show that the copy-number distribution of the mutant in generation n , conditioned on non-extinction until n , is described accurately by the deterministic increase from an initial distribution with mean 1. This distribution is related to the absolutely continuous part W + of the random variable, typically denoted W , that characterizes the stochasticity accumulating during the mutant's sweep. A suitable transformation yields the approximate dynamics of the mutant frequency distribution in a Wright–Fisher population of size N. Our expression provides a very accurate approximation except when mutant frequencies are close to 1. On this basis, we derive explicitly the (approximate) time dependence of the expected mean and variance of the trait and of the expected number of segregating sites. Unexpectedly, we obtain highly accurate approximations for all times, even for the quasi-stationary phase when the expected per-generation response and the trait variance have equilibrated. The latter refine classical results. In addition, we find that Θ is the main determinant of the pattern of adaptation at the genetic level, i.e., whether the initial allele-frequency dynamics are best described by sweep-like patterns at few loci or small allele-frequency shifts at many. The number of segregating sites is an appropriate indicator for these patterns. The selection strength determines primarily the rate of adaptation. The accuracy of our results is tested by comprehensive simulations in a Wright–Fisher framework. We argue that our results apply to more complex forms of directional selection. • Accurate and tractable time-dependent results at genetic and phenotypic level. • Explicit approximations for the initial phase of polygenic adaptation. • Refined classical, quantitative genetics results for the stationary phase. • Population-wide mutation rate characterizes genetic pattern of adaptation. • Number of segregating sites is an indicator of the pattern of adaptation. [ABSTRACT FROM AUTHOR]

We consider here two finite (arithmetic) mixture models (FMMs) with general parametric family of distributions. Sufficient conditions for the usual stochastic order and hazard rate order are then established under the assumption that the model parameter vectors are connected in p-larger order, reciprocal majorization order and weak super/sub majorization order. Furthermore, we establish hazard rate order and reversed hazard rate order between two mixture random variables (MRVs) when a matrix of model parameters and mixing proportions changes to another matrix in some mathematical sense. We have also considered scale family of distributions to establish some sufficient conditions under which the MRVs have hazard rate order. Several examples are presented to illustrate and clarify all the results established here. [ABSTRACT FROM AUTHOR]

Answering a pair of questions of Conrey, Gabbard, Grant, Liu, and Morrison, we prove that a triplet of dice drawn from the multiset model are intransitive with probability 1 / 4 + o (1) and the probability a random pair of dice tie tends toward α n - 1 for an explicitly defined constant α . This extends and sharpens the recent results of Polymath regarding the balanced sequence model. We further show the distribution of larger tournaments converges to a universal tournamenton in both models. This limit naturally arises from the discrete spectrum of a certain skew-symmetric operator (given by the kernel in the title acting on L 2 ([ - 1 , 1 ]) ). The limit exhibits a degree of symmetry and can be used to prove that, for instance, the limiting probability that A i beats A i + 1 for 1 ≤ i ≤ 4 and that A 5 beats A 1 is 1 / 32 + o (1) . Furthermore, the limiting tournamenton has range contained in the discrete set { 0 , 1 } . This proves that the associated tournamenton is non-quasirandom in a dramatic fashion, vastly extending work of Cornacchia and Hązła regarding the continuous analogue of the balanced sequence model. The proof is based on a reduction to conditional central limit theorems (related to work of Polymath), the use of a "Poissonization" style method to reduce to computations with independent random variables, and the systematic use of switching-based arguments to extract cancellations in Fourier estimates when establishing local limit-type estimates. [ABSTRACT FROM AUTHOR]

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

The research of convergence properties of moving average process is a challenging field of limit theorems. The aim of this article is to provide a method to prove the complete convergence and complete integral convergence of moving average process for independent random variables in sub-linear expectation space. The results obtained in the article are the extensions of some complete convergence theorems under classical probability space. [ABSTRACT FROM AUTHOR]

In this article, we consider smooth estimators for the quantile density function (qdf) for a sequence { X n , n ≥ 1 } of stationary non negative associated random variables with a common marginal distribution function. The qdf is given by q (u) = Q ′ (u) , u ∈ (0 , 1) , Q (u) representing the corresponding quantile function. The smooth estimators of q (u) considered here are adapted from those of Q (u) considered in Chaubey, Dewan, and Li (2021). A few asymptotic properties of these estimators are established parallel to those in the i.i.d. case. A numerical study comparing the mean squared errors of various estimators indicates the advantages and a few limitations of various estimators. The smoothing parameter is selected based on the BCV and RLCV (a variation of likelihood cross-validation) criteria. It is concluded, based on the numerical studies, that the RLCV criterion may produce over-smoothing, hence BCV criterion may be preferable. The numerical studies also suggest that, overall, the estimator proposed by Soni, Dewan, and Jain (2012) seems to have some advantage over the other estimators considered in this article. [ABSTRACT FROM AUTHOR]

We first consider the sequential detection of transient signals by generalizing the moving average chart to exponential family and study the false detection probability (FDP) and power of detection (POD) in the steady state. Then windowed adjusted signed (or modified directed) likelihood ratio chart is studied by treating it as approximate normal random variable. In the multi-parameter exponential family, the detection of the transient change of one of the canonical parameters or a function of canonical parameters is considered by using the generalized adjusted signed likelihood ratio chart. Comparisons with window restricted CUSUM and Shiryayev-Roberts (S-R) procedures show that the generalized signed likelihood ratio chart performs quite well. Several important examples including the mean or variance change under normal model and a real-time example are used for illustration. [ABSTRACT FROM AUTHOR]

The paper suggests a hybrid numerical method to price barrier options under Levy processes. As the main ingredient of our approach, we model the values of the Wiener-Hopf factors using artificial neural networks in the exact formula for the solution. The numerical Wiener-Hopf factorization typically reduces the problem to the factorization of the polynomial of exp(iξ), which is interpreted as the characteristic function of the random variable that approximates the Lévy process at the exponentially distributed time moment. We design and train a feedforward neural network with one hidden layer that approximates the coefficients of factors based on the input vector of the factorized polynomial coefficients. We implemented in the software a training data generator and a generalized loss function to factorize a polynomial of arbitrary degree. We demonstrate the performance of our approach using examples of factorization of second-, sixth- and 254th-degree polynomials. It takes a fraction of a second for our trained artificial neural networks to calculate the factors. [ABSTRACT FROM AUTHOR]

The importance of (probability) distributions in engineering science is undeniable. They are extensively used in this sector to carry out statistical studies and draw conclusions. In this article, we construct a new trigonometric distribution with support [ 0 , 1 ] called the truncated inverted arctan power (TIAP) distribution and demonstrate its use with engineering data. The corresponding probability density function is particularly flexible in the sense that it has various decreased right-skewness and unimodal forms. The associated hazard rate function shows that the TIAP distribution may adapt data with monotonic, U-shaped, and N-shaped failure rates. To reflect the interdependence of two random variables or sets of data, a bivariate variant of the TIAP distribution is also elaborated. All these distributional tools are then applied from a statistical perspective. In particular, the involved parameters are estimated using a maximum likelihood technique. Applications to engineering data indicate that the univariate and bivariate extensions for the TIAP distribution have a better fit compared to various current distributions. [ABSTRACT FROM AUTHOR]

Defining a probability model suitable for analyzing intricate and skewed real datasets holds significant importance in statistics. Here In this study, a novel class of models using the maximum of independent identical generalized Rayleigh random variables with the number of variables that have a power series class of distributions is proposed. This novel family of distributions contain several sub-models, including Poisson-generalized Rayleigh, geometric-generalized Rayleigh, binomial-generalized Rayleigh, and logarithmic-generalized Rayleigh models. The so obtained model can be unimodal and positively skewed, and it can be applied in modeling asymmetric data. We provide numerous distributional and statistical properties of this new family of distribution, notably, probability density, cumulative function, hazard rate function, k -moment, mean, variance, and quantile function. Different techniques consider the estimation of model parameters, likely maximum likelihood estimators, Expectation–Maximization (EM) and its Modified techniques, and extensive Monte Carlo (MC) simulation studies have been employed to see the efficiency of the suggested estimation techniques. At the end, three real data sets are analyzed for illustrative purposes. The results underscore the superior performance of the proposed Geom-GR model compared to its competitors, showcasing its effectiveness in accurately representing the analyzed datasets. [ABSTRACT FROM AUTHOR]

We study the competition complexity of dynamic pricing relative to the optimal auction in the fundamental single-item setting. In prophet inequality terminology, we compare the expected reward Am(F) achievable by the optimal online policy on m independent and identically distributed (i.i.d.) random variables distributed according to F to the expected maximum Mn(F) of n i.i.d. draws from F. We ask how big m has to be to ensure that (1+ε)Am(F)≥Mn(F) for all F. We resolve this question and characterize the competition complexity as a function of ε. When ε=0 , the competition complexity is unbounded. That is, for any n and m there is a distribution F such that Am(F)0 , it is sufficient and necessary to have m=ϕ(ε)n , where ϕ(ε)=Θ(log log 1/ε). Therefore, the competition complexity not only drops from unbounded to linear, it is actually linear with a very small constant. The technical core of our analysis is a lossless reduction to an infinite dimensional and nonlinear optimization problem that we solve optimally. A corollary of this reduction is a novel proof of the factor ≈0.745 i.i.d. prophet inequality, which simultaneously establishes matching upper and lower bounds. Funding: This work was supported by ANID (Anillo ICMD) [Grant ACT210005] and the Center for Mathematical Modeling [Grant FB210005]. [ABSTRACT FROM AUTHOR]

Treated as one of the popular measures in information theory, fuzzy mutual information quantifies the amount of information that one random variable has about another one. Different from standard mutual information, fuzzy mutual information can deal with not only discrete-valued but also real-valued variables. Therefore, fuzzy mutual information has been recently used in evolutionary filter feature selection approaches to measure the correlation between the classes and the features, and the dependencies within a feature set. Typically, this way can be considered as computationally efficient but sometimes it may not contribute to the performance of a classification algorithm. To address this issue, an improved evolutionary wrapper-filter approach which integrates an initialisation scheme and a local search module based on fuzzy mutual information in differential evolution is proposed. According to a number of experiments conducted on several real-world benchmark datasets, the proposed approach does not only significantly improve the computational efficiency of an evolutionary computation technique but also the performance of a classification algorithm. [ABSTRACT FROM AUTHOR]

A comparative analysis between Bidirectional Evolutionary Structural Optimization (BESO) and Smoothing-ESO (SESO), simultaneously considering Reliability-Based Topology Optimization (RBTO) and the structure's self-weight in the case of three-dimensional elasticity, is presented in this study. Due to the important role of the existence of uncertainties in making the structural design more realistic, geometry, volumetric fraction, modulus of elasticity, compliance, and loading are considered random variables with normal probability distribution. When adopting the First Order Reliability Method (FORM), the failure probability is calculated based on the reliability index. Furthermore, considering the influence of self-weight in problems involving large structures in civil engineering, especially in the case of bridges, this makes the optimal configuration more reliable for design. A series of examples are covered to validate the methods presented, showing their efficiency and robustness. [ABSTRACT FROM AUTHOR]

Distributed photovoltaic (PV) output exhibits strong stochasticity and weak adjustability. After being integrated with the network, its interaction with stochastic loads increases the difficulty of assessing the distribution network's static voltage stability (SVS). In response to this issue, this article presents a probabilistic assessment method for SVS in a distribution network with distributed PV that considers the bilateral uncertainties and correlations on the source and load sides. The probabilistic models for the uncertain variables are established, with the correlation between stochastic variables described using the Copula function. The three-point estimate method (3PEM) based on the Nataf transformation is used to generate correlated samples. Continuous power flow (CPF) calculations are then performed on these samples to obtain the system's critical voltage stability state. The distribution curves of critical voltage and load margin index (LMI) are fitted using Cornish-Fisher series. Finally, the utility function is introduced to establish the degree of risk of voltage instability under different scenarios, and the SVS assessment of the distribution network is completed. The IEEE 33-node distribution system is utilized to test the method presented, and the results across various scenarios highlight the method's effectiveness. [ABSTRACT FROM AUTHOR]

The CIR stochastic volatility model is modified to introduce nonlinear mean reversion, with the long-run volatility average as a random variable controlled by two parts being modeled through a Brownian motion and a Markov chain, respectively. This model still possesses an analytical formulation of the forward characteristic function, from which we establish variance swap prices as well as volatility swap ones with a nonlinear payoff in closed form. The numerical implementation of the two formulae demonstrates the significant impact of regime switching. [ABSTRACT FROM AUTHOR]

This research introduces min-max portfolio optimization models that incorporating transaction costs and focus on robust Entropic value-at-risk. This study offers a unified approach to handl the distribution of random parameters that affect the reward and risk aspects. Utilizing the duality theorem, the study transforms the optimization models into manageable forms, thereby accommodating the underlying random variables' discrete box and ellipsoidal distributions. The impact of transaction costs on optimal portfolio selection is examined through numerical examples under a robust return-risk framework. The results underscore the importance of the proposed model in safeguarding capital and reducing exposure to extreme risks, thus outperforming other strategies documented in the literature. This demonstrates the model's effectiveness in balancing maximizing returns and minimizing potential losses, making it a valuable tool for investors that seek to navigate uncertain financial markets. [ABSTRACT FROM AUTHOR]

In this research, we are examining the stochastic modified Korteweg-de Vries (SMKdV) equation forced in the Itô sense by multiplicative noise. We use an appropriate transformation to convert the SMKdV equation to another MKdV equation with random variable coefficients (MKdVRVCs). We use the generalizing Riccati equation mapping and Jacobi elliptic functions methods in order to acquire new trigonometric, hyperbolic, and rational solutions for MKdV-RVCs. After that, we can get the solutions to the SMKdV equation. To our knowledge, this is the first time we have assumed that the solution of the wave equation for the SMKdV equation is stochastic, since all earlier research assumed that it was deterministic. Furthermore, we provide different graphic representations to show the influence of multiplicative noise on the exact solutions of the SMKdV equation. [ABSTRACT FROM AUTHOR]

The paper contains the comparative analysis of the efficiency of different qunatile estimators for various distributions. Additionally, we show strong consistency of different quantile estimators and we study the Bahadur representation for each of the quantile estimators, when the sample is taken from NA, φ , ρ ∗ , ρ -mixing population. [ABSTRACT FROM AUTHOR]

In this paper, strong consistency of tail value-at-risk (TVaR) estimator under widely orthant dependent (WOD) samples is established, and a numerical simulation is performed to verify the validity of the theoretical results. To reveal the essence of the result, theoretical discussion on complete and complete moment convergence corresponding to the Baum–Katz law, as well as the Marcinkiewicz–Zygmund type strong law of large numbers (MZSLLN) for maximal weighted sums and maximal product sums of widely orthant dependent (WOD) random variables are investigated. The results obtained in the context extend the corresponding ones for independent and some dependent random variables. [ABSTRACT FROM AUTHOR]