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The 2022 International Symposium on Nonparametric Statistics was held in Paphos, Cyprus and co-sponsored by the Institute of Mathematical Statistics and the Bernoulli Society of Mathematical Statistics and Probability. The symposium brought together researchers from around the world to discuss recent advances and trends in nonparametric statistics. The conference covered a wide range of topics, including nonparametric estimation, hypothesis testing, adaptive inference, high-dimensional statistical inference, and more. The special issue of the Journal of Nonparametric Statistics contains papers that have undergone a peer review process and cover diverse areas of nonparametric statistics. [Extracted from the article]

Note, for instance, that the probabilities given by Castellares et al. ([1]) in page 4 are the same than those shown in expression (9.115) in the book by Johnson et al. ([3]), with the change of parameters Graph HT ht and Graph HT ht Neyman type A (NTA) distribution is frequently used in Biology, Biodosimetry, Environmental Sciences, Epidemiology, etc. A count random variable I X i is said to follow a stopped-sum Poisson, compound Poisson, multiple Poisson or clustered-Poisson distribution, if it can be represented as Graph HT ht where I N i is a Poisson random variable with parameter Graph HT ht and Graph HT ht are independent, identically distributed random variables that are also independent of I N i . [Extracted from the article]

This paper discussed the fuzzy reliability of pulping system in paper industry. Pulping system consists of four subsystems such as Digester, Knotter, Deckers, and Openers. These subsystems are working in series. In subsystems Knotter and Openers, one unit is operative and another unit is kept as cold standby. Fuzzy failure rates and fuzzy repair rates of the subsystems are taken as general. Trapezoidal fuzzy numbers are used to find out the reliability of the pulping system. Using Mehar’s method, the numerical results for reliability are obtained by considering exponential, Rayleigh, and Weibull distributions. On the basis of the results obtained in this study, it is suggested that paper industry management should involve Weibull distributed random variables for pulping system to attain higher reliability. [ABSTRACT FROM AUTHOR]

The paper has two main objectives. Firstly, it explores the properties of hyperbolic cosine and hyperbolic sine functions by using Volkenborn and the fermionic p-adic integrals, respectively. It also investigates interesting identities involving Bernoulli and degenerate Bernoulli numbers from differential equations with their solutions. Secondly, it introduces a random variable whose mass function is given in terms of Euler polynomials and find some expressions for the expectation of the random variable. [ABSTRACT FROM AUTHOR]

In this paper, the asymptotic normality and strong consistency for M estimators of the unknown regression coefficients in classical linear models are established under the assumptions that the errors are identically distributed φ-mixing random variables. The results obtained in this paper generalize the corresponding ones of Chen and Zhao [M-methods in linear model. Shanghai: Scientific and Technical Publishers; 1996] and Zhao [Strong consistency of M-estimates in linear model. Sci China Ser A. 2002;45:1420–1427] for independent errors. Finally, the simulation study is provided to verify the finite sample performance of the theoretical results and a real example is analysed for illustration. [ABSTRACT FROM AUTHOR]

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

This paper addresses the problem of H∞ performance analysis of 2D discrete singular stochastic system described by Roesser model which is challenging since it involves 2D random variables and the disturbance simultaneously. Sufficient conditions are established for the regularity, causality and stability of the system. The proposed results are expressed in terms of strict linear matrix inequalities. Furthermore, a mean square asymptotic stability with an $ H_{\infty } $ H ∞ disturbance level is developed. Simulation example is provided in order to illustrate the relevance of our approach. [ABSTRACT FROM AUTHOR]

This paper considers a repairable system whose periods of operations and repairs alternate during the run time. The residual lifetime of the system and its age, when the system operates at time $t$ t , are proposed, and their properties are investigated. Under the condition that the system is under repair, the remaining time until the end of system repair time and the elapsed time of a repair are studied. Since computing a renewal function is not straightforward, we use phase-type approximation to find the best-fitted distribution of corresponding random variables. We provide some examples and utilize a real data set to demonstrate the results. [ABSTRACT FROM AUTHOR]

This paper presents a flexible family of 2- and 3-parameter distributions whose support is the closed interval [0,1], with explicit density, cumulative density, and quantile functions. These distributions are suited to modeling quantiles, thereby expanding the toolbox of distributions for doubly-bounded random variables. The densities at the boundaries are determined by dispersion and skew parameters, and a third parameter exclusively influences location. The paper also discusses practical issues of parameter estimation and assesses estimation bias, Type I error-rate accuracy, and parameter-estimate collinearity. It also provides three examples of applications to real data using new packages implementing the distributions in R and Stata. [ABSTRACT FROM AUTHOR]

This paper proposes an efficient geotechnical reliability analysis framework that integrates the advantages of the first-order reliability method (FORM) and the Karhunen-Loève expansion (KL) to evaluate the reliability of spatially variable soil slopes. The improved Hasofer-Lind-Rackwitz-Fiessler (iHLRF) recursive algorithm is adopted to implement the FORM procedure when coupled with finite element codes for slope stability analysis, and the KL is used to reduce the dimension of random variables representing the soil random fields. To enhance the accuracy of the failure probability estimated by KL-iHLRF, the importance sampling (IS) is also conducted in this study, resulting in an innovative slope reliability analysis framework, KL-iHLRF-IS. It is found that although the FORM analysis by itself may not be able to confidently estimate the failure probability of spatially variable soil slopes because of the very high dimension of random variables and the strong nonlinearity of the limit state function, it provides useful information on the design point values for KL-iHLRF-IS to rapidly compute the failure probability. The efficiency of KL-iHLRF-IS for slope reliability analysis is illustrated by three example slope case studies. The proposed framework is particularly useful when fast yet accurate slope reliability analysis using the finite element method is needed. [ABSTRACT FROM AUTHOR]

This article mainly studies the strong convergence properties for randomly weighted maximum partial sums of arrays of row-wise extended negatively dependent (END, for short) random variables, including the complete moment convergence and complete f-moment convergence. The results obtained in this paper extend the corresponding ones in the literature. As an application, we investigate the complete consistency of the estimators of nonparametric regression models based on END random errors by using the complete convergence that we established. Then we provide comprehensive simulation studies to demonstrate the validity of the theoretical results based on the finite sample performance. Finally, an application to a real data set is illustrated. [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]

This special issue of the journal is a compilation of papers from the 41 SP st sp IAPSP Annual Conference entitled "Vienna-Kohut-Self Psychology: Searching for Creativity in Times of Crisis." Kottler and Ben co-create a unique, shared visual language in treatment, giving voice to Ben's less articulated and nascent self-states. As they work through their painful encounter, Kottler and Ben confront their largely hidden, alienated alter-ego self-states, "between different parts within a person and between people" (p. 74), which Togashi links to Buber's notion of I-Thou authentic dialogue. [Extracted from the article]

In this paper, the seven equivalent conditions of complete moment convergence and complete integral convergence for m -asymptotic negatively associated ( m -ANA, for short) random variables are established. The results obtained in the paper extend and improve some corresponding ones for negatively associated (NA, for short) random variables and negatively orthant dependent (NOD, for short) random variables. As an application of our main results, we present a result on complete consistency for the weighted estimator in a nonparametric regression model based on m-ANA errors. We perform a numerical simulation to verify the validity of the theoretical results. [ABSTRACT FROM AUTHOR]

The histogram has all its bin widths equal to some non-random number arbitrary set by an analyst (EBWH). In the result, particular bin counts are random variables. This paper presents also a histogram that is constructed in a converse manner. Bin counts are all equal to some non-random number arbitrary set by an analyst (EBCH). In the result, particular bin widths are random variables. The first goal of the paper is a choose of constant bin width (of bin numbers k) in the EBWH, which maximize the similarity measure in the Monte Carlo simulation. The second goal is a choose of constant bin count in the EBCH, which maximize the similarity measure in the Monte Carlo simulation. The third goal is to present similarity measures between empirical and theoretical data. The fourth goal is the comparative analysis of two histogram methods by means of the frequency formula. The first additional goal is a tip how to proceed in EBCH when modulo(n,k)≠0. The second additional goal is the software in the form of a Mathcad file with the implementation of EBWH and EBCH. [ABSTRACT FROM AUTHOR]

In this paper, we study the complete f-moment convergence for arrays of rowwise m-negatively associated random variables under some general conditions. The results obtained in the paper extend and improve some previous known ones. As an application of the main results, we present the complete consistency for the estimator in a semiparametric regression model based on m-negatively associated errors. We perform some numerical simulations to verify the validity of the theoretical results based on finite samples. [ABSTRACT FROM AUTHOR]

In this paper, complete moment convergence for maximum of randomly weighted sums and complete convergence for randomly indexed sums of martingale difference sequences (MDS) are investigated under some proper and sufficient conditions. A Marcinkiewicz–Zygmund type strong law of large numbers (MZSLLN) for MDS is obtained. In addition, relationships among weights, weight functions and boundary functions are revealed in a sense. The results obtained in the paper generalize some corresponding ones for independent and some dependent random variables. As an application, strong consistency for estimators in a nonparametric regression model is established. [ABSTRACT FROM AUTHOR]

In this paper, we define and study a stochastic SIR model on the class of regular rooted trees, in order to describe the spread of an epidemic on a closed population. A generalized geometric random variable is defined, which is essential for our study in this stochastic process. The main objective of this paper is to obtain the distribution of random variable X , the number of infected individuals at the stopping time that a diagnosis occurs. The analyses, simulations, and figures created with the software MATLAB certify the validity of the obtained results. [ABSTRACT FROM AUTHOR]

This paper is concerned with the $ H_{\infty } $ H ∞ resilient and event-triggered control of singular Markov jump systems against deception attacks. The deception attacks are modelled as a random bounded signal which is governed by a Bernoulli distributed random variable. The event-triggered scheme is adopted to achieve a trade-off between system performance and network resources. Based on the technique of stochastic Lyapunov–Krasovskii functionals and linear matrix inequalities, efficient criteria are developed such that the closed-loop system is stochastically admissible with a certain $ H_{\infty } $ H ∞ performance under deception attacks. Then, the co-design of resilient controller gains and event-triggered rules is provided in terms of a group of feasible LMIs. Finally, two examples are employed to verify the validity of our design. [ABSTRACT FROM AUTHOR]

In this paper we describe a methodology for parameter estimation of multivariate distributions defined as normal mean-variance mixture where the mixing random variable is rapidly decreasing tempered stable distributed. We address some numerical issues resulting from the use of the characteristic function for density approximation. We focus our attention on the practical implementation of numerical methods involving the use of these multivariate distributions in the field of finance and we empirical assess the proposed algorithm through an analysis on a five-dimensional series of stock index log-returns. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the complete f-moment convergence for weighted sums of asymptotically almost negatively associated (AANA, for short) random variables. Our results improve and generalize the corresponding ones of [M.M. Xi, X. Deng, X.J. Wang, and Z.Y. Cheng, L p convergence and complete convergence for weighted sums of AANA random variables, Commun. Stat. Theory Methods 47(22) (2018), pp. 5604–5613]. As an application of our main results, some results on the complete consistency for the estimator in semiparametric regression models are obtained and a simulation study is provided to assess the finite sample performance of the theoretical results. [ABSTRACT FROM AUTHOR]

During the last decades, several methods have been proposed for Kolmogorov-Smirnov one-sample test based on fuzzy random variables to describe the impression of classical random variables. However, such techniques do not discuss the modeling of imprecise observations and simulation of such data from the distribution of a fuzzy random variable. Moreover, such methods rely on a fuzzy cumulative distribution function with known parameters. In this paper, however, a modified Kolmogorov-Smirnov one-sample test is introduced based on a novel notion of fuzzy random variables which comes down to model fuzziness and randomness in the distribution of population in a frequently used family of probability distributions called location and scale distribution functions. A method of moment estimator was also utilized to estimate the location and scale parameters. Then, a notion of non-fuzzy Kolmogorov-Smirnov one-sample test was developed based on fuzzy hypotheses. Monte Carlo simulation was also employed to evaluate the critical value corresponding to a significance level and the performance of the test using power studies. Comparing the observed test statistics and the given fuzzy significance level, a classical procedure was finally used to accept or reject the null fuzzy hypothesis. Two numerical examples including a simulation study and an applied example were provided to clarify the discussions in this paper. The proposed method was also compared with some existing methods. The goodness-of-fit results demonstrated that the proposed Kolmogorov-Smirnov provides an efficient tool to handle statistical inference fuzzy observations. [ABSTRACT FROM AUTHOR]

Assembly and disassembly are important activities in the manufacturing/remanufacturing process. Although the line balancing problems of them have been extensively discussed in the existing literature, they are rarely integrated into one system. In this paper, a hybrid production line balancing problem is adopted while considering the similarity between the assembly and disassembly tasks. First, to better reflect the uncertainty existing in the actual production environment, a mathematical model of the multi-objective stochastic hybrid production line balancing problem is presented, in which task disassembly times are assumed to be random variables with known normal probability distributions. Then, a hybrid VNS-NSGA II algorithm combining variable neighbourhood search (VNS) and non-dominated sorting genetic algorithm II (NSGA II) is proposed to solve the problem. VNS is embedded into NSGA II as a local search to improve the quality of the solutions found by the NSGA II at each generation. Finally, the effectiveness of the proposed method is verified by a case study, and the superiority of hybrid production line is reflected by comparing the solutions of the independent production line with the hybrid production line. Computational comparisons demonstrate the potential benefits of the hybrid production line and the proposed method. [ABSTRACT FROM AUTHOR]

In many situations, it is common to have more than one observation per experimental unit, thus generating the experiments with repeated measures. In the modeling of such experiments, it is necessary to consider and model the intra-unit dependency structure. In the literature, there are several proposals to model positive continuous data with repeated measures. In this paper, we propose one more with the generalization of the beta prime regression model. We consider the possibility of dependence between observations of the same unit. Residuals and diagnostic tools also are discussed. To evaluate the finite-sample performance of the estimators, using different correlation matrices and distributions, we conducted a Monte Carlo simulation study. The methodology proposed is illustrated with an analysis of a real data set. Finally, we create an R package for easy access to publicly available the methodology described in this paper. [ABSTRACT FROM AUTHOR]

Non-negative limited normal or gamma distributed random variables are commonly used to model physical phenomenon such as the concentration of compounds within gaseous clouds. This paper demonstrates that when a collection of random variables with limited normal or gamma distributions represents a stationary process for which the underlying variables have exponentially decreasing correlations, then a central limit theorem applies to the correlated random variables. [ABSTRACT FROM AUTHOR]

We consider a storage process under the generalised order-up-to-level policy, based on a continuous-time Markov chain (CTMC). Specifically, the process starts at level S; whenever it drops to s, an order is sent, which is carried out after an exponential lead time. If during the lead time level S is reached, the order is cancelled, incurring some fee. This paper is written as an extension of Barron [2016. "An Fluid Inventory Model with Exponential Lead Times and Order Cancellations." Stochastic Models 32 (2): 301-332]. While the latter paper considered a fluid inventory model with backlogging and focused on discounted analysis only, the case of lost sales was not solved. The present paper generalises the analysis to incorporate unsatisfied demand for the expected discounted costs and for the average costs per time unit. We consider four costs. There is a fixed nonzero ordering cost or a fee for each order cancellation, a purchase cost for each ordered item, a storage cost for the stock, and a penalty cost due to the unmet demand. Applying renewal theory, multi-dimensional martingales, and stopping time theory, we obtain explicit expressions of the cost components. Numerical study provides several guidelines on the optimal controls. [ABSTRACT FROM AUTHOR]

This paper deals with the robust observer-based synchronisation problem for a class of complex dynamic networks subject to multi-weights, time-varying coupling delay and external disturbance. Specifically, the gain fluctuation appears in the proposed controller and is represented in terms of a random variable obeying the Bernoulli distribution. The main objective of this paper is to design a non-fragile memory state feedback controller such that the resulting error system is stochastically synchronised under a prescribed performance level . First, a Luenberger-type state observer is constructed to estimate the state variables of the addressed system. Second, by constructing an appropriate Lyapunov–Krasovskii functional and using Wirtinger-based integral inequality techniques, the required set of sufficient conditions for the synchronisation of the proposed system is established in the form of linear matrix inequalities. In the end, two numerical examples are provided to demonstrate the validity and feasibility of the developed theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, the complete convergence for maximum of weighted sums of widely negative orthant dependent (WNOD) random variables are investigated. Some sufficient conditions for the convergence are provided and a relationship between the weight and the boundary function is revealed. Additionally, a Marcinkiewicz-Zygmund type strong law of large number for weighted sums of WNOD random variables is obtained. The results obtained in this paper generalize some corresponding ones for independent and some dependent random variables. As an application, the strong consistency for the weighted estimator in a non-parametric regression model is established. MR(2010) Subject Classification: 60F15; 62G05. [ABSTRACT FROM AUTHOR]

Comfort on railway vehicles has been proven to depend on the number of passengers on the car, on their seating arrangement, as well as on the position in which it is assessed. The number of possible seating arrangement combinations is so large that comfort at a given location becomes a random variable even if passengers are considered deterministic vibration absorbers. In this paper we determine probability density functions (PDF) of comfort using a Monte Carlo scheme in which the number of passengers, their seating locations and their vibration characteristics (derived from passenger mass) are all random parameters with their own PDFs. Two types of distributions are obtained: the expected comfort of a single passenger and the compound comfort of all passengers on a given railway car. The carbody is represented by a beam model in which the first bending mode frequency has been allowed to vary so that the scope of results widens slightly. This variation is within the range of human sensitivity because this is the case in current lightweight construction, making carbody flexibility a key contributor to passenger comfort (or discomfort). Results confirm that comfort is indeed a stochastic variable with sizeable variance, and this prompts questions about the relation between the stochastic distribution and the tests prescribed in standard EN–12299. It will be shown that, surprisingly, comfort PDFs may be inferred with a high degree of accuracy (errors lower than 2%) from the tests in standard EN–12299. This is a most fortunate finding that radically transforms the interpretation of said standard, and allows rolling stock manufacturers and rail transport operators to have a much richer assessment of comfort on their vehicles from the same tests they now conduct, without having to perform Monte Carlo tests or simulations. [ABSTRACT FROM AUTHOR]

In order to detect radionuclides and dangerous substances in a fractured medium with the least amount of time and maximum probability, this paper provides a revolutionary tracking model. It relies on a coordinated tracking strategy using set of programmed nano-sensors. The radionuclide particle has a linear flow from d-directions to spread in a single direction with Random Walk process. We assume that this particle has been spread over a short period of time along phantomic cylindrical path inside the fluid. Two nano-sensors will track or search along each cylinder's route, starting from any location in the fragmented medium (space). A vector of random variables with a known probability distribution makes up the particle's initial position. We add the discounted effort-reward track as a reduction parameter in the distance function. The expected value of the first meeting time between one of the nano-sensors and a Random walk target will be reduced as a result. We extract various supplementary results regarding the optimal tracking strategy in addition to presenting the analytical solution that demonstrates the existence of a finite tracking technique. [ABSTRACT FROM AUTHOR]

The strong limit theory is one of the most important problems in the probability theory. Some results on the convergence of ρ ˜ -mixing random sequences have been presented. In this paper, we study the almost sure convergence for ρ ˜ -mixing random sequences. As a result, we generalize partial results of Wu and Jiang [Wu, Q. Y., and Y. Y. Jiang. 2008. Some strong limit theorems for q ˜ -mixing sequences of random variables. Statistics & Probability Letters 78:1017–23.]. We obtain the mainstream and some corresponding conclusions by using truncation methods and the generalized three-series theorem. A known result is generalized in this paper. [ABSTRACT FROM AUTHOR]

This paper is concerned with the consistency of nonparametric regression model. For the weighted estimator of unknown regression function, the strong consistency, the complete consistency and the convergence rate of the complete consistency are investigated under some mild conditions. These results extend or improve the corresponding ones of Yang et al. (2018) for extended negatively dependent (END, for short) random variables to asymptotically almost negatively associated random variables. Also, the simulation study of the finite samples provided in this paper shows the validity of our results. [ABSTRACT FROM AUTHOR]

In this paper, we address the distributed resilient fusion filtering (DRFF) problem for a class of nonlinear multi-sensor networked systems (MSNSs) with random sensor delay (RSD) under round-robin protocol (RRP). The RSD is depicted by the Bernoulli random variable with known occurrence probability. In order to relieve the network congestion, the RRP that can deal with information overload issue of the transmission process from sensor to the estimator is utilised. The major objective of this paper is that the resilient fusion filter is designed for nonlinear MSNSs with RSD and RRP in the light of the inverse covariance intersection approach, where the local upper bound regarding the filtering error covariance is obtained and then minimised by suitably exploiting the local filter gain. Finally, a simulation example that can show the validity of the provided DRFF algorithm is presented. [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]

The local limit theorem (LLT) is one of the well-known limit theorems which can be used to estimate the probability at a particular point of a random variable. In this paper, we generalize weighted sums which are introduced by Giuliano and Weber and give the LLT with explicit error bounds. [ABSTRACT FROM AUTHOR]

Support vector machine (SVM) is a supervised machine-learning method which can be used for both classification and regression models. In this paper, we introduce a new model of SVM which any of training samples containing inputs and outputs are considered the random variables with known probability functions. The SVM is first converted into equivalent quadratic programming (QP) formulations in linear and nonlinear cases. An artificial neural network for SVM learning is then proposed. The presented neural network framework guarantees to obtain the optimal solution of the SVM problem. The existence and convergence of the trajectories of the network are studied. The Lyapunov stability for the considered neural network is also shown. The efficiency of the proposed method is shown by four illustrative examples. [ABSTRACT FROM AUTHOR]

In this paper, we establish the complete moment convergence for a field of martingale difference random variables, weakly upper bounded by a random variable. The results generalize and extend the complete convergences for non-identically distributed martingale-difference random fields to the case of complete moment convergences. [ABSTRACT FROM AUTHOR]

In this paper, we mainly study the asymptotic normality of wavelet estimators in the heteroscedastic regression model with φ-mixing errors. Under some suitable conditions, the asymptotic normality of the wavelet estimators of g and f in the heteroscedastic regression model with φ-mixing errors are obtained, which generalize or improve the corresponding ones for α-mixing random variables and martingale difference sequence in some sense. Also, the simulation study of the finite samples provided in this paper shows the validity of our results. [ABSTRACT FROM AUTHOR]

The reliability analysis for the system with degradation and random shocks is an important issue in the field of reliability engineering. In this paper, we use Wiener process to fit the performance degradation process, and regard both the degradation rate and the mean of the magnitude of shock load as random variables which follow the truncated normal distribution. With the Markov Chain Monte Carlo(MCMC), we provide a new method to estimate the parameters of the reliability function of the system. At the end of the paper, we take the degradation and shock data of the MOSFET as an example to show the effectiveness of the method presented in the paper. [ABSTRACT FROM AUTHOR]

In this paper, we present some new ordering properties between two parallel systems comprising general independent heterogeneous components. More precisely, let X 1 , ⋯ , X n and Y 1 , ⋯ , Y n be independent non-negative random variables with X i ∼ F (x ; α i , β i) and Y i ∼ F (x ; θ i , λ i) , i = 1 , ⋯ , n , where F (.) is an absolutely continuous distribution function with reversed hazard rate function r ˜ (·). In this paper, under certain conditions, by using the concept of vector majorization, unordered order, p-majorization and related orders, we discuss stochastic comparisons between parallel systems in the sense of usual stochastic and reversed hazard rate orders. The results developed in this paper generalize some known results in the literature. [ABSTRACT FROM AUTHOR]

This paper obtains an asymptotic formula for the finite-time ruin probability of the compound nonhomogeneous Poisson risk model with a constant interest force, in which the claims are conditionally independent random variables with a common subexponential distribution. The paper also obtains some asymptotic relations of randomly weighted sums ∑ i = 1 n θ i X i , in which the weights θi i = 1 , 2 , ⋯ , n are positive random variables which are bounded above and the primary random variables Xi, i = 1 , 2 , ⋯ , n are conditionally independent and follow subexponential distributions. [ABSTRACT FROM AUTHOR]

Main purpose of this paper is to study a robust measure of estimating dependence between random variables that can be used as an alternative to classical covariance estimator. An efficient univariate nested L-estimator (repeated median) Sn with high breakdown point is used to define bivariate dispersion. Results regarding in the characteristics of proposed estimator is discussed through this paper. [ABSTRACT FROM AUTHOR]

In this paper, we study the weak convergence and convergence rate in the weak law of large numbers for weighted sums of a class of random variables satisfying the Rosenthal type inequality. The necessary and sufficient conditions for the convergence rates in the weak law of large numbers under some mild conditions are provided. Moreover, the main results that we established are applied to simple linear errors-in-variables regression models and nonparametric regression models based on a class of random errors. Finally, we present some numerical simulations to assess the finite sample performance of the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the tampered random variable (TRV) modeling in multiple step-stress life testing experiments. Here τ 1 < τ 2 < ... < τ k − 1 be (k − 1) prespecified time points and s 1 , s 2 , ... , s k be k prefixed stress levels with si being the stress level in force during the time interval [ τ i − 1 , τ i) for i = 1 , ... , k with τ 0 = 0 and τ k = ∞. We define the tampered random variable T TRV (k) in multiple step-stress scenario and calculate the PDF, CDF, and Hazard rate for the proposed tampered variable T TRV (k) . We derive a general expression for the expectation of T TRV (k) under different number k of stress levels and also obtain some results on stochastic ordering for different k. All these results are obtained under arbitrary baseline (under normal stress condition with stress level s1) life distribution. In particular, we consider exponential distribution with mean θ and Weibull distribution with scale parameter λ and shape parameter α for specific expressions. We also prove some results on equivalence of the TRV modeling with the two other existing models for step-stress life testing, namely, cumulative exposure and tampered failure rate. Finally, we consider some variations of the modeling approach for T TRV (k) to include incorporation of the stress levels, discrete life time, bivariate or multivariate life times. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the pth moment exponential stability of stochastic differential equations driven by G-Brownian motion (G-SDEs) with respect to a part of the variables by means of the G-Lyapunov functions and recently developed Itô's calculus for SDEs driven by G-Brownian motion, as well as Gronwall's inequalities. We establish sufficient conditions to ensure the quasi sure exponential stability of stochastic differential equations perturbed by G-Brownian motion with respect to a part of the variables. Some illustrative examples to show the usefulness of the stability with respect to a part of the variables notion are also provided. [ABSTRACT FROM AUTHOR]

In this paper, we mainly establish a general form of Berry–Esséen bound for α-mixing random variables. With different choices of the parameters, the rates are shown as O (n − 3 / 26) , O (n − 1 / 6) , and approximately O (n − 1 / 4). These results improved some corresponding ones in the literature. An application to the Berry–Esséen bound of sample quantiles is further provided. Moreover, some simulations are also carried out to support the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we establish L2-convergence and complete convergence results for the maximum of the partial sum of asymptotically negatively associated random vectors in Hilbert space. In addition, we consider Hájek-Rényi inequality and prove some strong law of large numbers for H-valued asymptotically negatively associated random vectors. [ABSTRACT FROM AUTHOR]

Discrete kernel smoothing is now gaining importance in nonparametric statistics. In this paper, we investigate some asymptotic properties of the normalised discrete associated-kernel estimator of a probability mass function and make comparisons. We show, under some regularity and non-restrictive assumptions on the associated-kernel, that the normalising random variable converges in mean square to 1. We then derive the consistency and the asymptotic normality of the proposed estimator. Various families of discrete kernels already exhibited satisfy the conditions, including the refined CoM-Poisson which is underdispersed and of second-order. Finally, the first-order binomial kernel is discussed and, surprisingly, its normalised estimator has a suitable asymptotic behaviour through simulations. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to investigate the practical stability in relation to a part of the variables of stochastic reaction–diffusion systems driven by G-Brownian motion (G-SRDSs, in short). With the aid of G-Lyapunov techniques and G-Itô's formula, the criteria of the global practical uniform kth moment exponential stability and the global practical uniform quasi surely exponential stability in relation to a part of variables of G-SRDSs are established. An example is given to illustrate the usefulness and feasibility of the proposed results. [ABSTRACT FROM AUTHOR]

In this paper, we use the non-negative discrete semimartingale convergence theorems to study the stochastic theta methods with random stepsizes to reproduce the almost sure stability of the exact solution of stochastic differential equations. Moreover, the choice of the stepsize in each step is based on the stochastic theta methods of random variable stepsize. In numerical experiments, we propose an algorithm that successfully use θ-Maruyama and θ-Milstein methods to simulate the numerical solutions of stochastic differential equations, reproduce the almost sure stability of exact solutions of SDEs and simulate the random variable stepsize in each timestep, and compared with constant stepsizes, random stepsize can speed up the decay process and reduce the iterations greatly. [ABSTRACT FROM AUTHOR]