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In his article Willems (Clim Chang 120(4):931-944, ) proposed a methodology to analyse extremes in rainfall series. When applying it to artificially generated, non-cyclic random variables we were able to detect cyclic behavior. Therefor we had a closer look on the methodology. Here we discuss our considerations, why this method generates cycles, depending on chosen subperiods and their coherence between detected cycle lengths. To verify these relationships some examples based on random data samples are given. [ABSTRACT FROM AUTHOR]

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

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

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

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

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

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

Theoretical analysis and empirical study results all show that there are situations in reality where observed data are not random variables. Thus, decision-making criteria based on probability theory are not suitable for people to make decisions. This paper proposes an uncertain dominance based on uncertainty theory to offer an alternative decision-making criterion for such situations. The paper first defines a new criterion of first- and second-order uncertain dominance, then proves some necessary conditions of them based on uncertainty theory. Some sufficient and necessary conditions of the first- and second-order uncertain dominance are given when uncertain variables are all normal or linear uncertain variables. In addition, the paper proves the link between the uncertain dominance criterion and the expected utility criterion and shows that the first-order uncertain dominance is suitable for all people to make decisions and the second-order uncertain dominance is suitable for risk-averse people to make decisions. [ABSTRACT FROM AUTHOR]

The generalized Kaiser–Bessel window function is defined via the modified Bessel function of the first kind and arises frequently in tomographic image reconstruction. In this paper, we study in details the properties of the Kaiser–Bessel distribution, which we define via the symmetric form of the generalized Kaiser–Bessel window function. The Kaiser–Bessel distribution resembles to the Bessel distribution of McKay of the first type, it is a platykurtic or sub-Gaussian distribution, it is not infinitely divisible in the classical sense and it is an extension of the Wigner's semicircle, parabolic and n-sphere distributions, as well as of the ultra-spherical (or hyper-spherical) and power semicircle distributions. We deduce the moments and absolute moments of this distribution and we find its characteristic and moment generating function in two different ways. In addition, we find its cumulative distribution function in three different ways and we deduce a recurrence relation for the moments and absolute moments. Moreover, by using a formula of Ismail and May on quotient of modified Bessel functions of the first kind, we deduce a closed-form expression for the differential entropy. We also prove that the Kaiser–Bessel distribution belongs to the family of log-concave and geometrically concave distributions, and we study in details the monotonicity and convexity properties of the probability density function with respect to the argument and each of the parameters. In the study of the monotonicity with respect to one of the parameters we complement a known result of Gronwall concerning the logarithmic derivative of modified Bessel functions of the first kind. Finally, we also present a modified method of moments to estimate the parameters of the Kaiser–Bessel distribution, and by using the classical rejection method we present two algorithms for sampling independent continuous random variables of Kaiser–Bessel distribution. The paper is closed with conclusions and proposals for future works. [ABSTRACT FROM AUTHOR]

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

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

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

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

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

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

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

In the current paper, we review existing tools for solving variable selection problems in psychology. Modern regularization methods such as lasso regression have recently been introduced in the field and are incorporated into popular methodologies, such as network analysis. However, several recognized limitations of lasso regularization may limit its suitability for psychological research. In this paper, we compare the properties of lasso approaches used for variable selection to Bayesian variable selection approaches. In particular we highlight advantages of stochastic search variable selection (SSVS), that make it well suited for variable selection applications in psychology. We demonstrate these advantages and contrast SSVS with lasso type penalization in an application to predict depression symptoms in a large sample and an accompanying simulation study. We investigate the effects of sample size, effect size, and patterns of correlation among predictors on rates of correct and false inclusion and bias in the estimates. SSVS as investigated here is reasonably computationally efficient and powerful to detect moderate effects in small sample sizes (or small effects in moderate sample sizes), while protecting against false inclusion and without over-penalizing true effects. We recommend SSVS as a flexible framework that is well-suited for the field, discuss limitations, and suggest directions for future development. [ABSTRACT FROM AUTHOR]

In this paper, we study bounds for the total variation distance between distributions of second order polynomials in normal random variables provided that they essentially depend on at least three variables. Moreover, we partially extend some recent bounds for the Kolmogorov distance between the distributions of norms of Gaussian random vectors to the case of the total variation distance. [ABSTRACT FROM AUTHOR]

In this paper, we assume that cause–effect relationships between random variables can be represented by a Gaussian linear structural equation model and the corresponding directed acyclic graph. Then, we consider a situation where a set of random variables that satisfies the front-door criterion is observed to estimate a total effect. In this situation, when the ordinary least squares method is utilized to estimate the total effect, we formulate the unbiased estimator of the causal effect on the variance of the outcome variable. In addition, we provide the exact variance formula of the proposed unbiased estimator. [ABSTRACT FROM AUTHOR]

In this paper, we obtain an approximation for the distribution function of sum of two independent random variables using quantile based representation. The error of approximation is shown to be negligible under some mild conditions. We then use the approximation to obtain a non-parametric estimator for the distribution function of sum of two independent random variables. The exact distribution of the proposed estimator is derived. The estimator is shown to be strongly consistent and asymptotically normally distributed. Extensive Monte Carlo simulation studies are carried out to evaluate the bias and mean squared error of the estimator and also to assess the approximation error. We also compare the performance of the proposed estimator with other estimators available in the literature. Finally, we illustrate the use of the proposed estimator for estimating the reliability function of a standby redundant system. [ABSTRACT FROM AUTHOR]

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

Quantum-behaved Particle Swarm Optimization (QPSO) is a meta-heuristic optimization algorithm, which is widely used in many research fields and practical problems due to its flexibility and low computational cost. However, the existing QPSO algorithms and their variants still have problems such as insufficient search capabilities, lack of adaptivity, and prone to stagnation. This paper proposes a novel ensemble algorithm, ACQPSOW-HGS, based on Quantum-behaved Particle Swarm Optimization (QPSO) and Hunger Games Search (HGS). By combining three improvements and introducing three hybrid strategies, our algorithm has made a comprehensive development, effectively improving the stability and solution accuracy in a large number of test functions and the parameter identification application, which is superior compared with many existing algorithms. First, we design the Weibull distribution random number generation operator, the distance-guided adaptive control technique, and the chaotic update mechanism to deal with the weak randomness, insufficient adaptability, and susceptibility to stagnation of the original QPSO algorithm, respectively. Integrating the above improvements, ACQPSOW is proposed as an improved variant of QPSO. Second, the proposed ensemble algorithm ACQPSOW-HGS is built on ACQPSOW and HGS and combined with specific hybrid strategies to add population diversity and improve search efficiency, including the Selection-Crossover-Mutation mechanism, the elite local search mechanism, and the information exchange mechanism. Finally, the experiments, on 23 benchmark functions and the IEEE CEC 2017 test suite, demonstrate that ACQPSOW-HGS outperforms comparison algorithms in terms of convergence speed and solution accuracy through non-parametric statistical tests. Moreover, ACQPSOW-HGS was applied to the fractional-order hyper-chaotic financial system for parameter identification to illustrate the applicability and robustness in solving real-world problems. [ABSTRACT FROM AUTHOR]

Demand-side flexible load resources, such as Electric Vehicles (EVs) and Air Conditioners (ACs), offer significant potential for enhancing flexibility in the power system, thereby promoting the full integration of renewable energy. To this end, this paper proposes an optimal allocation method for demand-side flexible resources to enhance renewable energy consumption. Firstly, the adjustable flexibility of these resources is modeled based on the generalized energy storage model. Secondly, we generate random scenarios for wind, solar, and load, considering variable correlations based on non-parametric probability predictions of random variables combined with Copula function sampling. Next, we establish the optimal allocation model for demand-side flexible resources, considering the simulated operation of these random scenarios. Finally, we optimize the demand-side resource transformation plan year by year based on the growth trend forecast results of renewable energy installed capacity in Jiangsu Province from 2025 to 2031. [ABSTRACT FROM AUTHOR]

In reliability theory, the kth order statistic represents the lifetime of a (n - k + 1) -out-of-n system. In particular, the smallest (largest) order statistics denotes the lifetime of a series (parallel) system that consist of n components; and the second smallest (second largest) order statistics is the lifetime of a (n - 1) -out-of-n (2-out-of-n) system. In this paper, sufficient conditions are provided to compare the smallest and the second smallest (largest and second largest) order statistics of dependent and heterogeneous random variables having the additive hazard model with the Archimedean copula in the sense of usual stochastic order and hazard rate order. Further, we compare the smallest order statistics of two sets of independent and heterogeneous random variables having the additive hazard model in the sense of dispersive order. Finally, our theoretical findings are evaluated by some numerical examples and counterexamples. [ABSTRACT FROM AUTHOR]

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

Blockchain technology brings about an opportunity to maintain decentralization in several applications, such as cryptocurrency. With the agents of a decentralized system operating independently, it calls for a consensus protocol that helps all nodes to agree on the state of the ledger. Most of the existing blockchains rely on Proof of Work (PoW) as the underlying consensus algorithm, resulting in a significant amount of electricity power consumption. Furthermore, it demands the miner to buy specific computation devices. Besides, a protocol to gather the society-related taxes such as public education funding and charities is lacking in existing consensus algorithms. In response, this paper proposes a new consensus algorithm, namely Proof of Humanity (PoH) aiming at gathering society-related taxes. According to PoH, the probability that an agent becomes a leader depends on its donations to non-profit accounts. Therefore, PoH encourages miners to donate money and gain mining power, its incentives, and transaction fees. The associated bureaucracy model is introduced briefly to address the required ecosystem for real case implementation of PoH. A distributed random variable generation algorithm is presented in this paper which ensures that the randomly selected leader is neither predictable nor adjustable. It is demonstrated that the proposed blockchain is totally robust against forking and possesses a high level of propagation speed, which ensures the scalability. Simulations show that the proposed blockchain network does not fail even in adverse scenarios where the majority of nodes refuse to propagate valid blocks. Besides, simulations reveal a suitable average block creation duration. [ABSTRACT FROM AUTHOR]

This paper investigates the outlier-resistant variance-constrained H ∞ state estimation problem for a class of discrete time-varying recurrent neural networks with randomly occurring deception attacks. The randomly occurring deception attacks are modeled by a series of random variables satisfying the Bernoulli distribution with known probability. In addition, the saturation function is introduced to reduce the negative impact from the measurement outliers onto the estimation performance. The objective of this paper is to propose an outlier-resistant finite-horizon state estimation scheme without utilizing the augmentation method such that, in the presence of measurement outliers and randomly occurring deception attacks, some sufficient criteria are obtained ensuring both the desired H ∞ performance index and the error variance boundedness. Finally, a numerical example is used to illustrate the feasibility of the presented outlier-resistant variance-constrained H ∞ state estimation algorithm. [ABSTRACT FROM AUTHOR]

As a type of coronavirus, COVID-19 has quickly spread around the majority of countries worldwide, and seriously threatens human health and security. This paper aims to depict cumulative numbers of COVID-19 infections in China using the growth model chosen by cross validation. The residual plot does not look like a null plot, so we can not find a distribution function for the disturbance term that is close enough to the true frequency. Therefore, the disturbance term can not be characterized as random variables, and stochastic regression analysis is invalid in this case. To better describe this pandemic automatically, this paper first employs uncertain growth models with the help of uncertain hypothesis tests to detect and modify outliers in data. The forecast value and confidence interval for the cumulative number of COVID-19 infections in China are provided. [ABSTRACT FROM AUTHOR]

Consider a class of discrete probability distributions with a limited support. A typical example of such support is some variant of a Likert scale, with a response mapped to either the { 1 , 2 , ... , 5 } or { - 3 , - 2 , ... , 2 , 3 } set. Such type of data is common for Multimedia Quality Assessment but can also be found in many other research fields. For modelling such data a latent variable approach is usually used (e.g., Ordered Probit). In many cases it is convenient or even necessary to avoid latent variable approach (e.g., when dealing with too small sample size). To avoid it the proper class of discrete distributions is needed. The main idea of this paper is to propose a family of discrete probability distributions with only two parameters that play the same role as the parameters of the normal distribution. We call the new class the Generalised Score Distribution (GSD). The proposed GSD class covers the entire set of possible means and variances, for any fixed and finite support. Furthermore, the GSD class can be treated as an underdispersed continuation of a reparametrized beta-binomial distribution. The GSD class parameters are intuitive and can be easily estimated by the method of moments. We also offer a Maximum Likelihood Estimation (MLE) algorithm for the GSD class and evidence that the class properly describes response distributions coming from 24 Multimedia Quality Assessment experiments. At last, we show that the GSD class can be represented as a sum of dichotomous zero–one random variables, which points to an interesting interpretation of the class. [ABSTRACT FROM AUTHOR]

This paper addresses certain distributional aspects of a scale-free scatter matrix denoted by R that is stemming from a matrix-variate gamma distribution having a positive definite scale parameter matrix B. Under the assumption that B is a diagonal matrix, a structural representation of the determinant of R is derived; the exact density functions of products and ratios of determinants of matrices possessing such a structure are obtained; a closed form expression is given for the density function of R. Moreover, a novel procedure is utilized to establish that certain functions of the determinant of the sample scatter matrix are asymptotically distributed as chi-square or normal random variables. Then, representations of the density function of R that respectively involve multiple integrals, multiple series and Gauss' hypergeometric function are provided for the general case of a positive definite scale parameter matrix, and an illustrative numerical example is presented. Cutting-edge mathematical techniques have been employed to derive the results. Naturally, they also apply to the conventional sample correlation matrix which is encountered in various multivariate inference contexts. [ABSTRACT FROM AUTHOR]

We consider uncertainty quantification for the Poisson problem subject to domain uncertainty. For the stochastic parameterization of the random domain, we use the model recently introduced by Kaarnioja et al. (SIAM J. Numer. Anal., 2020) in which a countably infinite number of independent random variables enter the random field as periodic functions. We develop lattice quasi-Monte Carlo (QMC) cubature rules for computing the expected value of the solution to the Poisson problem subject to domain uncertainty. These QMC rules can be shown to exhibit higher order cubature convergence rates permitted by the periodic setting independently of the stochastic dimension of the problem. In addition, we present a complete error analysis for the problem by taking into account the approximation errors incurred by truncating the input random field to a finite number of terms and discretizing the spatial domain using finite elements. The paper concludes with numerical experiments demonstrating the theoretical error estimates. [ABSTRACT FROM AUTHOR]

In this paper, we study properties of a series–parallel system. The component lifetimes may be dependent and non-identically distributed (DNID) discrete random variables. We consider the number of failed components upon system failure. We derive the probability mass function and the expected value of this quantity. In addition, we find the conditional probabilities corresponding to this variate given some partial information about the system failure. We also provide a numerical example to demonstrate the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we consider two k-out-of-n systems comprising heterogeneous dependent components under random shocks, with an Archimedean copula. We then provide sufficient conditions on the distributions of components' lifetimes and the generator of the Archimedean copula and on the random shocks for comparing the lifetimes of two systems with respect to the usual stochastic order. Finally, we present some examples to illustrate the established results. [ABSTRACT FROM AUTHOR]

In this paper, a new class of distributions called the T-X θ family of distributions for bounded—(0,1)—and unbounded— (0 , ∞) —supported random variables is suggested. Some special sub-models of the proposed family are utilized. A new sub-model is selected to be studied in details. The statistical properties of the suggested family including quantile function, moments, moment generating function, order statistics and Rényi entropy are discussed. The maximum likelihood method is provided to estimate the parameters of the distribution and a Monte Carlo simulation study is used. The discretized T-X θ family provided many sub-families and sub-models. In addition, eight real data sets are utilized to demonstrate the flexibility of the proposed continuous and discrete family's multiple sub models. [ABSTRACT FROM AUTHOR]

In this paper, we consider the H ∞ state estimation issue under variance constraint for recurrent neural networks with time-varying parameters, where the time-delay as well as randomly occurring sensor nonlinearity are handled and the communication is scheduled by round-robin protocol. The phenomenon of randomly occurring sensor nonlinearity is modeled by a random variable obeying the Bernoulli distribution with known probability. In order to alleviate unnecessary network congestion in communication channels, the round-robin protocol is introduced to specify which network node has the right to access the network channel at each time step. In particular, the objective is to develop the time-varying state estimation method such that, in the presence of time-delay, randomly occurring sensor nonlinearity and round-robin protocol, the sufficient conditions are given and both the error variance boundedness and the pre-set H ∞ performance index can be achieved simultaneously. In the end, we provide a simulation example with comparison tests to demonstrate the feasibility of presented H ∞ state estimation method. [ABSTRACT FROM AUTHOR]

Statistical inference is the process of drawing conclusions about underlying population(s) using sample data to either confirm or falsify hypotheses. However, the complexity of real-life problems often makes the underlying statistical models inadequate, as information is often imprecise in many respects. To address this common problem, some papers have been published on modifications and extensions of test concepts by employing tools of fuzzy statistics. In this paper, we present a non-parametric test for the difference between quantiles of two independent populations based on fuzzy random variables. For this purpose, we consider the fuzzy quantile function and its estimation based on α -values of fuzzy random variables. We then provide a fuzzy test based on the fuzzy empirical distribution function for the difference of fuzzy order statistics from these independent populations. We also suggest a specific degree-based criterion to compare the fuzzy test statistics at a specific significance level to decide whether the underlying fuzzy null hypothesis can be rejected or not. The effectiveness of the proposed two-sample test on quantiles is investigated via numerical examples. [ABSTRACT FROM AUTHOR]

In this paper, we obtain lower and upper bounds for the Gini mean difference for the case of independent and identically distributed random variables based on the information about mean, variance, skewness, and kurtosis of the distribution. We also obtain some relationships between the three dispersion measures in the general case. The established results improve some well-known bounds and inequalities. These results are then used to sharpen some inequalities concerning Gini's index, order statistics and premium principles. Examples demonstrate that the proposed bounds perform much better than the existing ones. [ABSTRACT FROM AUTHOR]

This paper discusses the issue of partial-neurons-based H ∞ state estimation for time-varying recurrent neural networks subject to randomly occurring time delays under variance constraint index. The measurement outputs are allowed to be available only at certain neurons. In addition, a random variable is introduced to model the randomly occurring time delays with certain occurrence probability. The aim is to propose the non-augmented partial-neurons-based state estimation strategy. Accordingly, some sufficient conditions are given to ensure two indices including the pre-determined H ∞ performance index and the error variance boundedness via the stochastic analysis approach. Finally, a simulation example is used to demonstrate the feasibility of presented partial-neurons-based H ∞ state estimation algorithm. [ABSTRACT FROM AUTHOR]

This paper is a continuation of our recent paper (Electron. J. Probab., 24(141), (2019)) and is devoted to the asymptotic behavior of a class of supercritical super Ornstein-Uhlenbeck processes (Xt)t≥0 with branching mechanisms of infinite second moments. In the aforementioned paper, we proved stable central limit theorems for Xt(f) for some functions f of polynomial growth in three different regimes. However, we were not able to prove central limit theorems for Xt(f) for all functions f of polynomial growth. In this note, we show that the limiting stable random variables in the three different regimes are independent, and as a consequence, we get stable central limit theorems for Xt(f) for all functions f of polynomial growth. [ABSTRACT FROM AUTHOR]

In this paper, we give an almost sure central limit theorem (ASCLT) version of a maximum limit theorem (MLT) with an arbitrary sequence {dn, n ≥ 1} of weighted means of max{Xk, k ∈ An}, where {Xn, n ≥ 1} is a sequence of independent random variables, and {An, n ≥ 1} is a sequence of almost surely finite random subsets of positive integers independent of {Xn, n ≥ 1}. Thus we generalize the cases considered in the literature: (i) the nonrandom version of ASCLT for the MLT; (ii) the version of ASCLT for randomly indexed MLT; and (iii) the version of maximum schema of observed and unobserved random variables. We complete the paper with illustrative examples. [ABSTRACT FROM AUTHOR]

The aim of this paper is to investigate the possible impact of foreign direct investment inflows (FDI) on environmental pollution and to test the validity of the pollution haven hypothesis (PHH) in the case of Turkey over the period 1970–2020. For this purpose, we apply the Fourier approximation to determine stochastic properties of the variables that are FDI, economic growth, energy consumption, and CO2 emissions used in empirical analysis and the relationship between them. The advantage of the Fourier approximation is capable of capturing possible structural breaks in unknown forms and numbers in the series. According to Fourier KPSS and Fourier FADF tests, all series are stationary at order one, I (1). Fourier Shin and Fourier ADL cointegration tests put forth evidence of the existence of a long-term relationship between CO2, GDP, EC, and FDI. FMOLS expanded with Fourier terms suggesting that FDI has relatively little but a positive impact on CO2 emissions, so we conclude that PHH is valid for Turkey. The other finding reveals that there exists an inverted U-shape relationship between economic growth and CO2 emissions. According to this result, the environmental Kuznets curve (EKC) hypothesis for Turkey is also supported. Another remark of this paper is that energy consumption significantly increases environmental degradation in Turkey. These findings also are supported by Fourier Toda and Yamamoto causality test. There is a causality relationship from GDP, EC, and FDI to CO2 emissions. These findings offer useful recommendations for policymakers: the FDI, which uses new and clean technology, should be encouraged and implemented energy policies should be energy intensity reducer and efficiency increaser for reducing environmental pollution in Turkey. [ABSTRACT FROM AUTHOR]

When analyzing the stability of a slope reinforced by frame-anchors, this paper establishes a calculation model of slope stability by using the vertical slice method, and derives the stability performance function. In order to make up the shortcomings of the traditional deterministic calculation method, regarding the physical parameters of the soil as random variables, the slope stability is calculated based on the reliability theory. Applying the method to an engineering example, the reliability index of the overall stability of the slope under the failure of a single anchor is calculated. Finally, by applying the finite element software, GeoStudio, the reliability of the stability in the engineering example is analyzed, and the two methods are compared and evaluated. The results show that the failure of the anchor near the foot of the slope has the greatest impact on the stability of the slope. The theoretical calculations are in good agreement with the numerical simulation results. The proposed method is effective for the stability calculation of slopes reinforced by frame-anchors. The impact of the failure of a single anchor cannot be ignored, especially the anchors at the foot of the slope, whose design should follow the principle of "strengthening foot and waist" to avoid the hidden danger to the overall stability brought about by the failure of the anchor. [ABSTRACT FROM AUTHOR]

In this paper, we first establish a Kesten-type inequality for randomly weighted sums, in which the primary random variables are assumed to be real-valued and subexponential following a general dependence structure proposed by J. Geluk and Q. Tang [Asymptotic tail probabilities of sums of dependent subexponential random variables, J. Theor. Probab., 22(4):871–882, 2009], and the random weights are assumed to be nonnegative and arbitrarily dependent but independent of the primary random variables. The obtained result extends the work of Y. Chen [A Kesten-type bound for sums of randomly weighted subexponential random variables, Stat. Probab. Lett., 158:108661, 2020]. Then, as an application, we derive an asymptotic formula for finite-time ruin probability of a renewal risk model with constant force of interest and dependent by-claims. [ABSTRACT FROM AUTHOR]

In this paper, we obtain equivalent conditions of complete moment convergence of the maximum for partial weighted sums of independent identically distributed random variables under sublinear expectations space. The results obtained in the paper are extensions of the equivalent conditions of complete moment convergence of the maximum under classical linear expectation space. [ABSTRACT FROM AUTHOR]

This paper proposes a multi-level dynamic factor model to identify common components in output gap estimates. We pool multiple estimates for 157 countries and decompose them into one global, eight regional, and 157 country-specific cycles. Our approach easily deals with mixed frequencies, ragged edges, and discontinuities in the underlying output gap estimates. To restrict the parameter space in the Bayesian state space model, we apply a stochastic search variable selection approach and base the prior inclusion probabilities on spatial information. Our results suggest that the global and the regional cycles explain a substantial proportion of the output gaps. On average, 18% of a country's output gap is attributable to the global cycle, 24% to the regional cycle, and 58% to the local cycle. [ABSTRACT FROM AUTHOR]

In the recent JAVELIN Bladder 100 phase 3 trial, avelumab plus best supportive care significantly prolonged overall survival relative to best supportive care alone as first-line maintenance therapy following first-line platinum-based chemotherapy in patients with advanced urothelial cancer (aUC). Discovering biomarkers using genomic profiling to understand potential patient heterogeneity is essential to help improve patient care with precision medicine. For the JAVELIN Bladder 100 trial, it is unclear which variable selection methods can most reliably identify biomarkers to inform patient care because the dataset is characterized by high collinearity and low signal. The aim of this paper was to evaluate available selection methods and their ability to discover prognostic and predictive biomarkers in patients with aUC receiving first-line maintenance therapy. A simulation study evaluated the performance of popular variable selection approaches for high-dimensional data, including penalized regression models, random survival forests, and Bayesian variable selection methods. For Bayesian variable selection methods, a modified Bayesian Information Criterion (BIC) thresholding rule was proposed in addition to the traditional BIC thresholding rule. These methods were applied to the JAVELIN Bladder 100 dataset to investigate potential biomarkers associated with survival benefit. Results from the simulations demonstrated the strengths and limitations of the different methods. The variable selection methods demonstrated low false discovery rates under different conditions. However, their performance declined in the presence of high collinearity. Using the JAVELIN Bladder 100 data, we identified some potentially significant biomarkers across multiple models. Several lasso-related methods were able to identify potentially biologically meaningful variables in the trial. Some variable selection methods (such as stochastic search variable selection and random survival forest) may not be well suited to this type of data due to the presence of extreme collinearity and low signal. Future research should explore novel variable selection methods that may be more suitable for identifying prognostic and predictive biomarkers in this population. Trial registration: ClinicalTrials.gov Identifier: NCT02603432. [ABSTRACT FROM AUTHOR]

We consider the problem of approximating a continuous random variable, characterized by a cumulative distribution function (cdf) F(x), by means of k points, x 1 < x 2 < ⋯ < x k , with probabilities p i , i = 1 , ⋯ , k . For a given k, a criterion for determining the x i and p i of the approximating k-point discrete distribution can be the minimization of some distance to the original distribution. Here we consider the weighted Cramér-von Mises distance between the original cdf F(x) and the step-wise cdf F ^ (x) of the approximating discrete distribution, characterized by a non-negative weighting function w(x). This problem has been already solved analytically when w(x) corresponds to the probability density function of the continuous random variable, w (x) = F ′ (x) , and when w(x) is a piece-wise constant function, through a numerical iterative procedure based on a homotopy continuation approach. In this paper, we propose and implement a solution to the problem for different choices of the weighting function w(x), highlighting how the results are affected by w(x) itself and by the number of approximating points k, in addition to F(x); although an analytic solution is not usually available, yet the problem can be numerically solved through an iterative method, which alternately updates the two sub-sets of k unknowns, the x i 's (or a transformation thereof) and the p i 's, till convergence. The main apparent advantage of these discrete approximations is their universality, since they can be applied to most continuous distributions, whether they possess or not the first moments. In order to shed some light on the proposed approaches, applications to several well-known continuous distributions (among them, the normal and the exponential) and to a practical problem where discretization is a useful tool are also illustrated. [ABSTRACT FROM AUTHOR]

For a sequence of multi-state trials with l possible outcomes denoted by 1 , 2 , ... , l , let E be the event that at least k 1 consecutive 1s followed by at least k 2 consecutive 2s,..., followed by at least k l consecutive ls. Denote by T r the number of trials for the rth occurrence of the event E in a sequence of multi-state trials. This paper studies the distribution of the waiting time random variable T r when the sequence consists of independent and identically distributed multi-state trials. In particular, distributional properties of T r are examined via matrix-geometric distributions. [ABSTRACT FROM AUTHOR]

In this paper, we study the asymptotic distribution of the maxima of suprema of dependent Gaussian processes with trend. For different scales of the time horizon we obtain different normalizing functions for the convergence of the maxima. The obtained results not only have potential applications in estimating the delay of certain Gaussian fork-join queueing systems but also provide interesting insights to the extreme value theory for triangular arrays of random variables with row-wise dependence. [ABSTRACT FROM AUTHOR]

In this paper, we prove a local limit theorem and a refined continuity correction for the negative binomial distribution. We present two applications of the results. First, we find the asymptotics of the median for a NegativeBinomial (r , p) random variable jittered by a Uniform (0 , 1) , which answers a problem left open in Coeurjolly and Trépanier (Metrika 83(7):837–851, 2020). This is used to construct a simple, robust and consistent estimator of the parameter p, when r > 0 is known. The case where r is unknown is also briefly covered. Second, we find an upper bound on the Le Cam distance between negative binomial and normal experiments. [ABSTRACT FROM AUTHOR]