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Dimensionality Reduction (DR) is the process of reducing the numerous features or random variables under consideration to a limited number of features by obtaining a set of principal variables. These techniques cater great values in machine learning, which come in handy to simplify a classification or a regression dataset, thereby yielding a better-performing predictive model. Techniques used for DR include Feature Selection methods, Matrix Factorization, AutoEncoder methods, and Manifold Learning. Merits of DR include data compression, reduced space of storage, and removal of redundant features. This paper attempts to review various techniques used to carry out dimensionality reduction while providing an exhaustive comparative study over the merits and demerits of each of the techniques used under the empirical experiments performed by the authors whose work is being reviewed. [ABSTRACT FROM AUTHOR]

Obeid and Kadry (2019) tried to study the product and quotient of the independent Pareto and Rayleigh random variables. The distributions they obtained are incorrect and in fact there is no closed form distributions as discussed here. We will mention the errors made and try to establish the correct versions of the probability density functions of these distributions for the truncated Pareto and Rayleigh random variables. [ABSTRACT FROM AUTHOR]

• The citations of 729,515 articles fit by the generalized extreme-value distribution. • The complexity of references and citations of papers' quantiles is studied. • The macroscopic model of the citation distribution is proposed. The paper presents an in-depth study of uncited papers. For that, we explore the documents indexed in the INSPIRE database from 1970 to 2015. Uncited articles represent a complex bibliometric environment in which references are generated. The reference lists of uncited papers form a dynamic system partially responsible for the redistribution of scientific impact. Our task is to quantify the detailed structure of citations and references directly in terms of quantiles. We also study the entropy and the statistical complexity measure of references and citations of papers' quantiles. We introduce a theoretical framework in which citation distribution is considered an asymptotic distribution of the largest values in a sequence of independent identically distributed random variables. We show that this asymptotic distribution is the generalized extreme-value distribution. Furthermore, we empirically demonstrate that the asymptotic behavior of citation distribution is close to (but not quite) the generalized extreme-value distribution. [ABSTRACT FROM AUTHOR]

A new robust Kalman filter (KF) based on mixing distribution is presented to address the filtering issue for a linear system with measurement loss (ML) and heavy-tailed measurement noise (HTMN) in this paper. A new Student's t -inverse-Wishart-Gamma mixing distribution is derived to more rationally model the HTMN. By employing a discrete Bernoulli random variable (DBRV), the form of measurement likelihood function of double mixing distributions is converted from a weighted sum to an exponential product, and a hierarchical Gaussian state-space model (HGSSM) is therefore established. Finally, the system state, the intermediate random variables (IRVs) of the new STIWG distribution, and the DBRV are simultaneously estimated by utilizing the variational Bayesian (VB) method. Numerical example simulation experiment indicates that the proposed filter in this paper has superior performance than current algorithms in processing ML and HTMN. [ABSTRACT FROM AUTHOR]

We consider a principal who periodically offers a fixed and costly nonmonetary reward to agents to incentivize them to invest effort over the long run. An agent's output, as a function of his effort, is a priori uncertain and is worth a fixed per-unit value to the principal. The principal's goal is to design an attractive reward policy that specifies how the rewards are to be given to an agent over time based on that agent's past performance. This problem, which we denote by P , is motivated by practical examples from both academia (e.g., a reduced teaching load) and industry (e.g., "Supplier of the Year" awards). The following "limited-term" (LT) reward policy structure has been quite popular in practice. The principal evaluates each agent periodically; if an agent's performance over a certain (limited) number of periods in the immediate past exceeds a predefined threshold, then the principal rewards him for a certain (limited) number of periods in the immediate future. When agents' outputs are deterministic in their efforts, we show that there always exists an optimal policy that is an LT policy and also, obtain such a policy. When agents' outputs are stochastic, we show that the class of LT policies may not contain any optimal policy of problem P but is guaranteed to contain policies that are arbitrarily near optimal. Given any ϵ > 0 , we show how to obtain an LT policy whose performance is within ϵ of that of an optimal policy. This guarantee depends crucially on the use of sufficiently long histories of the agents' outputs. We also analyze LT policies with short histories and derive structural insights on the role played by (i) the length of the available history and (ii) the variability in the random variable governing an agent's output. We show that the average performance of these policies is within 5% of the optimum, justifying their popularity in practice. We then introduce and analyze the class of "score-based" reward policies; we show that this class is guaranteed to contain an optimal policy and also, obtain such a policy. Finally, we analyze a generalization in which the principal has a limited number for rewards in any given period and show that the class of score-based policies, with modifications to accommodate the limited availability of the rewards, continues to contain an optimal solution for the principal. This paper was accepted by Jeannette Song, operations management. Supplemental Material: The online appendix is available at https://doi.org/10.1287/mnsc.2022.4482. [ABSTRACT FROM AUTHOR]

Most peer-evaluation practices rely on the evaluator’s goodwill and model them as potentially noisy evaluators. But what if graders are competitive, i.e., enjoy higher utility when their peers get lower scores? We model the setting as a multi-agent incentive design problem and propose a new mechanism, PEQA, that incentivizes these agents (peer-graders) through a score-assignment rule and a grading performance score. PEQA is designed in such a way that it makes grader-bias irrelevant and ensures grader-utility to be monotonically increasing with the grading-precision, despite competitiveness. When grading is costly and costs are private information of the individual graders, a modified version of PEQA implements the socially optimal grading-choices in equilibrium. Data from our classroom experiments is consistent with our theoretical assumptions and show that PEQA outperforms the popular median mechanism, which is used in several massive open online courses (MOOCs). [ABSTRACT FROM AUTHOR]

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 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 framework of this paper was intertemporal choice, that is to say, the process whereby people were required to choose between a smaller-sooner reward and a larger-later income. In this study, the selection of rewards was supported by a discount function instead of direct preferences between the involved rewards. The objective of this paper was to measure the discounting concentration of a discount function through a variant of the Gini index and the Lorenz curve usually used in statistics. Both measures allowed for the comparison of the discounting concentration corresponding to two discount functions. The methodology employed in this paper was based on the parallelism between a discount function and the distribution function of an absolutely continuous random variable. This similarity allowed us to export the measures of concentration from the field of statistics to finance. The main result of this work was the analysis of the discounting concentration depending on other characteristics of the shape of a discount function (regularity and super-additivity) and the total area under the discount function curve. [ABSTRACT FROM AUTHOR]

The article focuses on the system reliability analysis of steel trusses (plane and spatial). The computations are realized by the use of a developed by the author C++ code. The following loads are taken into account: self-weight, weight of coverings, wind and snow. The limit state function is defined as a difference between the bearing capacity and the effect of action of an element. The paper presents how effective tool is the system reliability analysis compared with traditional structural design methods. The methods of transforming Gumbel distribution into normal and generating random variables are described. [ABSTRACT FROM AUTHOR]

Nowadays, one of the main challenges facing green innovation management is how to enhance the performance of innovation processes by utilizing asymmetric input and output data. Therefore, this paper develops an improved SBM model analysis framework for evaluating the green innovation efficiency of asymmetric input and output data. The framework is applied to assess the technical (TE), managerial (PTE), and scale (SE) efficiencies of new energy companies under three input variables (R&D personnel input, R&D capital input, and comprehensive energy consumption input), two desirable output variables (green technology output and economic output), and one undesirable output variable (greenhouse gas emissions). Then, environmental factors and random factors are eliminated from the obtained input slack variables based on the SFA model, placing decision-making units in a homogeneous environment. The results demonstrate that TE, PTE, and SE are improved after eliminating environmental factors and random factors. Subsequently, based on the entropy method, this paper classifies companies' green innovation patterns into four categories and provides targeted solutions. The purpose of this paper is to provide an evaluation method for new energy companies to understand green innovation efficiency and assist decision makers in identifying the most optimal resource allocation approach. The proposed improved SBM model contributes to the literature and to industry practice by (1) providing a reliable evaluation of green innovation efficiency under asymmetric input and output data; (2) determining effective improvement actions based on a slack analysis of environmental variables and random variables that lead to improved process performance; and (3) making fuzzy innovation performance efficient to facilitate understanding and managing innovation resource allocation quality. [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]

This paper introduces a novel three-parameter skew-log-logistic distribution. The research involves the development of a new random variable based on Azzalini and Capitanio's (2013) proposition. Additionally, various statistical properties of this distribution are explored. The paper presents a maximum likelihood method for estimating the distribution's parameters. The density function exhibits unimodality with heavy right tails, while the hazard function exhibits rapid increase, unimodality, and slow decrease, resulting in a right-skewed curve. Furthermore, four real datasets are utilized to assess the applicability of this new distribution. The AIC and BIC criteria are employed to assess the goodness of fit, revealing that the new distribution offers greater flexibility compared to the baseline distribution. [ABSTRACT FROM AUTHOR]

We would like to point out that the formula for the cumulative distribution given in Coelho-Barros et al. (2017) and a similar version of it given in Usman et al. (2021) are not cumulative distribution functions as these functions do not satisfy the one or more necessary and sufficient conditions for a function to be a cumulative distribution function. We would also like to mention that formulas for the cumulative distribution functions of product and ratio of two independent Pareto and Exponential random variables given by Obeid and Kadry (2022) are not cumulative distribution functions either. We do not believe that these formulas can be fixed to be cumulative distribution functions. In this short article, we provide mathematical justification in support of these claims. [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 this paper we consider two random variables in a cell in the network of mobile users. The first random variable (RV) is the distance of active mobile user from a base station. The second RV is emission power for the random active user if the control of emission power exists. RV emission power is dependent RV of the first RV. That's why the calculations of mean values for these RVs differ one from the other. The first RV depends only on the users' density area distribution. The second RV depends on the signal attenuation value in the considered environment. It is proved that, in real conditions, emission power to a user at the mean value of distance from a base station is always lower than mean value of emission power to a user. The difference between these two power values increases as the signal attenuation coefficient increases. These two values are calculated for three characteristic user density distributions in a cell. The results are verified by original computer simulation programs. [ABSTRACT FROM AUTHOR]

The authors study the complete convergence and complete moment convergence for weighted sums of m-extended negatively dependent (m-END) random variables. The results obtained in this paper extend and improve the corresponding results of Wu, Zhai and Peng [Y. F. Wu, M. Q. Zhai and J. Y. Peng, On the complete convergence for weighted sums of extended negatively dependent random variables, Journal of Mathematical Inequalities, 13 (1) (2019), 251–260] and Zarei and Jabbari [H. Zarei and H. Jabbari, Complete convergence of weighted sums under negative dependence, Statistical Papers, 52 (2011), 413–418]. [ABSTRACT FROM AUTHOR]

U-statistics represent a fundamental class of statistics arising from modeling quantities of interest defined by multi-subject responses. U-statistics generalize the empirical mean of a random variable X to sums over every m-tuple of distinct observations of X. Stute [182] introduced a class of so-called conditional U-statistics, which may be viewed as a generalization of the Nadaraya-Watson estimates of a regression function. Stute proved their strong pointwise consistency to: r(m)(φ, t) ≔ 피[φ(F1,..., Ym)|(X1,..., Xm) = t], for t ∈ Xm. In this paper, we are mainly interested in the study of the kNN conditional U-processes in a functional mixing data framework. More precisely, we investigate the weak convergence of the conditional empirical process indexed by a suitable class of functions and of the kNN conditional U-processes when the explicative variable is functional. We treat the uniform central limit theorem in both cases when the class of functions is bounded or unbounded satisfying some moment conditions. The second main contribution of this study is the establishment of a sharp almost complete Uniform consistency in the Number of Neighbors of the constructed estimator. Such a result allows the number of neighbors to vary within a complete range for which the estimator is consistent. Consequently, it represents an interesting guideline in practice to select the optimal bandwidth in nonparametric functional data analysis. These results are proved under some standard structural conditions on the Vapnik-Chervonenkis classes of functions and some mild conditions on the model. The theoretical results established in this paper are (or will be) key tools for further functional data analysis developments. Potential applications include the set indexed conditional U-statistics, Kendall rank correlation coefficient, the discrimination problems and the time series prediction from a continuous set of past values. [ABSTRACT FROM AUTHOR]

Frequent natural disasters challenge relief network efficiency. This paper introduces a stochastic relief network with limited path capacity, develops an equilibrium model based on cumulative prospect theory, and formulates it as a stochastic variational inequality problem to enhance emergency response and resource allocation efficiency. Using the NCP function, Lagrange function, and random variables, the model dynamically monitors disasters, enabling rational resource allocation for quick decision-making. Compared to traditional methods, our model significantly improves resource scheduling and reduces disaster response costs. Through a random network example, we validate the model's effectiveness in aiding intelligent decision-making for relief plans and resource allocation optimization. [ABSTRACT FROM AUTHOR]

In this paper we use the Riemann zeta distribution to give a new proof of the Erdös-Kac Central Limit Theorem. That is, if \zeta (s)=\sum _{n\ge 1} \frac {1}{n^s}, s>1, then we consider the random variable X_s with P(X_s=n)=\frac {1}{\zeta (s)n^s}, n\ge 1. In an earlier paper, the first author and Adrien Peltzer derived the analog of the Erdös-Kac Central Limit Theorem (CLT) for the number of distinct prime factors, \omega (X_s), of X_s, as s\searrow 1. In this paper we show, by means of a Tauberian Theorem, how to obtain the Central Limit Theorem of Erdös-Kac for the uniform distribution from the result for the random variable X_s. We also apply the technique to the number of distinct prime divisors of X_s that lie in an arithmetic sequence and a local CLT of the type proved by Dixit and Murty [Hardy-Ramanujan J. 43 (2020), 17–23] as well a version of the CLT for irreducible divisors of a monic polynomial over a finite field. [ABSTRACT FROM AUTHOR]

In this paper, we find conditions under which distribution functions of randomly stopped minimum, maximum, minimum of sums and maximum of sums belong to the class of generalized subexponential distributions. The results presented in this article complement the closure properties of randomly stopped sums considered in the authors' previous work. In this work, as in the previous one, the primary random variables are supposed to be independent and real-valued, but not necessarily identically distributed. The counting random variable describing the stopping moment of random structures is supposed to be nonnegative, integer-valued and not degenerate at zero. In addition, it is supposed that counting random variable and the sequence of the primary random variables are independent. At the end of the paper, it is demonstrated how randomly stopped structures can be applied to the construction of new generalized subexponential distributions. [ABSTRACT FROM AUTHOR]

This paper discusses the dissipative filtering problem for discrete-time nonlinear networked systems with dynamic quantization and data packet dropouts. The Takagi–Sugeno (T–S) fuzzy model is employed to approximate the considered nonlinear plant. Both the measurement and performance outputs are assumed to be quantized by the dynamic quantizers before being transmitted. Moreover, the Bernoulli stochastic variables are utilized to characterize the effects of data packet dropouts on the measurement and performance outputs. The purpose of this paper is to design full- and reduced-order filters, such that the stochastic stability and dissipative filtering performance for the filtering error system can be guaranteed. The collaborative design conditions for the desired filter and the dynamic quantizers are expressed in the form of linear matrix inequalities. Finally, simulation results are used to illustrate the feasibility of the proposed filtering scheme. [ABSTRACT FROM AUTHOR]

Let X1, X2, . . ., Xn be a sequence of coherent random variables, i.e., satisfying the equalities Xj = P(A|Gj), j = 1, 2, . . ., n, almost surely for some event A. This paper contains the proof of the estimate P (max 1=i

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]

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In recent years, uncertainty analysis is a hot topic in the field of electromagnetic compatibility simulation. The actual electromagnetic environment is simulated by considering the randomness of the model input parameters. However, there are currently two key issues that have not been resolved. One is the curse of dimensionality problem that occurs when there are many random variables. The other is how to establish a random input model with generality and portability. In order to address these issues, this paper proposes a new random input modeling method called random variable black box model. When applying to the Stochastic Collocation Method with dimensionality reduction sparse grid strategy, the applicability of this uncertainty analysis method can be extended to any probability density function, then enabling efficient electromagnetic compatibility simulation uncertainty analysis of high-dimensional random variable models and fundamentally solving the curse of dimensionality problem. Finally, this paper implements a joint simulation technology of the MATLAB software and COMSOL software to verify the strong portability of the random variable black box model, ensuring that advanced uncertainty analysis methods can be smoothly introduced into commercial electromagnetic simulation software and expanding the application scope of uncertainty analysis. [ABSTRACT FROM AUTHOR]

In this paper, the asmptotics is considered for the distribution tail of a randomly stopped sum Sν = X1 + ··· + Xν of independent identically distributed consistently varying random variables with zero mean, where ν is a counting random variable independent of {X1,X2, . . .}. The conditions are provided for the relation P(Sν > x) ∼ Eν P(X1 > x) to hold, as x →∞, involving the finiteness of E|X1|. The result improves that of Olvera-Cravioto [14], where the finiteness of a moment E|X1|r for some r > 1 was assumed. [ABSTRACT FROM AUTHOR]

This paper analyses the disruptions occurring in a production system determining the operating states of a single machine. A system with a convergent production character, in which both single flows (streams) and multi-stream flows occur, was considered. In this paper, a two-level formalisation of the production system (PS) was made according to complex systems theory. The continuity analysis was performed at the operational level (manufacturing machine level). The definition of the kth survival value and the quasi-coherence property defined on chains of synchronous relations were used to determine the impact of interruption of the processed material flow on uninterrupted machine operation. The developed methodology is presented in terms of shaping the energy efficiency of technical objects with the highest power demand (the furnace of an automatic paint shop and the furnace of a glass tempering line were taken into consideration). The proposed methodology is used to optimise energy consumption in complex production structures. The model presented is utilitarian in nature—it can be applied to any technical system where there is randomness of task execution times and randomness of unplanned events. This paper considers the case in which two mutually independent random variables determining the duration of correct operation T P and the duration of breakdown T B are determined by a given distribution: Gaussian and Gamma family distributions (including combinations of exponential and Erlang distributions). A formalised methodology is also developed to determine the stability of system operation, as well as to assess the potential risk for arbitrary system evaluation parameters. [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]

In this paper we study the Marcinkiewicz–Zygmund-type strong law of large numbers with general normalizing sequences under sublinear expectation. Specifically, we establish complete convergence in the Marcinkiewicz–Zygmund-type strong law of large numbers for sequences of negatively dependent and identically distributed random variables under certain moment conditions. We also give results for sequences of independent and identically distributed random variables. The moment conditions in this paper are based on a class of slowly varying functions that satisfy some convergence properties. Moreover, some special examples and comparisons to existing results are also given. [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]

Background: Simulation is an important tool for assessing the performance of statistical methods for the analysis of data and for the planning of studies. While methods are available for the simulation of correlated binary random variables, all have significant practical limitations for simulating outcomes from longitudinal cluster randomised trial designs, such as the cluster randomised crossover and the stepped wedge trial designs. For these trial designs as the number of observations in each cluster increases these methods either become computationally infeasible or their range of allowable correlations rapidly shrinks to zero. Methods: In this paper we present a simple method for simulating binary random variables with a specified vector of prevalences and correlation matrix. This method allows for the outcome prevalence to change due to treatment or over time, and for a 'nested exchangeable' correlation structure, in which observations in the same cluster are more highly correlated if they are measured in the same time period than in different time periods, and where different individuals are measured in each time period. This means that our method is also applicable to more general hierarchical clustered data contexts, such as students within classrooms within schools. The method is demonstrated by simulating 1000 datasets with parameters matching those derived from data from a cluster randomised crossover trial assessing two variants of stress ulcer prophylaxis. Results: Our method is orders of magnitude faster than the most well known general simulation method while also allowing a much wider range of correlations than alternative methods. An implementation of our method is available in an R package NestBin. Conclusions: This simulation method is the first to allow for practical and efficient simulation of large datasets of binary outcomes with the commonly used nested exchangeable correlation structure. This will allow for much more effective testing of designs and inference methods for longitudinal cluster randomised trials with binary outcomes. [ABSTRACT FROM AUTHOR]

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

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

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]

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]

This paper generalizes the concept of capacity from the portfolio level to the investment process for systematic equity strategies. Capacity is often understood as the maximum asset under management, above which additional inflows would have too great a negative impact on performance. The concept of capacity is often limited to the study of a given portfolio. However, setting up a capacity management framework must consider what the portfolio might look like in the future. This is obviously complicated for discretionary portfolios but theoretically conceivable for portfolios implementing systematic strategies, if we can simulate all possible scenarios. In our framework, we extend the traditional definition of capacity from a number to a random variable, allowing portfolio managers to integrate it into their risk considerations. We provide examples of how portfolio managers can approach this problem, with full-search or modelling methods. Our framework includes several capacity metrics that can be used jointly or selected to align better with the features of each strategy. [ABSTRACT FROM AUTHOR]

This paper analyzes the co-fluctuation between a scalar response random variable and a curve regressor using quantile regression. We focus on the situation wherein the output variable is observed with random missing. For this incomplete functional data situation, we estimate the quantile regression by combining two principal nonparametric methods: the local linearity approach (LLA) and the kernel nearest neighbor (KNN) algorithm. We study the asymptotic properties of the constructed estimator by establishing, under general assumptions, uniform consistency over the number of neighborhoods. This asymptotic result provides good mathematical support for the selection of the optimal neighborhood. We examine the feasibility of the constructed estimator using artificially generated data. Moreover, we apply the quantile regression technique in food quality by predicting the riboflavin quantity in yogurt using spectrometry data. [ABSTRACT FROM AUTHOR]

Rooted in dynamic systems theory, convergent cross mapping (CCM) has attracted increased attention recently due to its capability in detecting linear and nonlinear causal coupling in both random and deterministic settings. One limitation with CCM is that it uses both past and future values to predict the current value, which is inconsistent with the widely accepted definition of causality, where it is assumed that the future values of one process cannot influence the past of another. To overcome this obstacle, in our previous research, we introduced the concept of causalized convergent cross mapping (cCCM), where future values are no longer used to predict the current value. In this paper, we focus on the implementation of cCCM in causality analysis. More specifically, we demonstrate the effectiveness of cCCM in identifying both linear and nonlinear causal coupling in various settings through a large number of examples, including Gaussian random variables with additive noise, sinusoidal waveforms, autoregressive models, stochastic processes with a dominant spectral component embedded in noise, deterministic chaotic maps, and systems with memory, as well as experimental fMRI data. In particular, we analyze the impact of shadow manifold construction on the performance of cCCM and provide detailed guidelines on how to configure the key parameters of cCCM in different applications. Overall, our analysis indicates that cCCM is a promising and easy-to-implement tool for causality analysis in a wide spectrum of applications. [ABSTRACT FROM AUTHOR]

Cyber-security research on networked multi-sensor systems is crucial due to the vulnerability to various types of cyberattacks. For the development of effective defense measures, attention is required to gain insight into the complex characteristics and behaviors of cyber attacks from the attacker's perspective. This paper aims to tackle the problem of distributed consensus estimation for networked multi-sensor systems subject to hybrid attacks and missing measurements. To account for both random denial of service (DoS) attacks and false data injection (FDI) attacks, a hybrid attack model on the estimator-to-estimator communication channel is presented. The characteristics of missing measurements are defined by random variables that satisfy the Bernoulli distribution. Then a modified consensus-based distributed estimator, integrated with the characteristics of hybrid attacks and missing measurements, is presented. For reducing the computational complexity of the optimal distributed estimation method, a scalable suboptimal distributed consensus estimator is designed. Sufficient conditions are further provided for guaranteeing the stability of the proposed suboptimal distributed estimator. Finally, a simulation experiment on aircraft tracking is executed to validate the effectiveness and feasibility of the proposed algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we investigate an extended version of the elephant random walk model. Unlike the traditional approach where step sizes remain constant, our model introduces a novel feature: step sizes are generated as a sequence of positive independent and identically distributed random variables, and the step of the walker at time n+1 depends only on the steps of the walker between times 1, ..., mn, where (mn)n⩾1 is a sequence of positive integers growing to infinity as n goes to infinity. Our main results deal with the validity of the central limit theorem for this new variation of the standard ERW model introduced by Schutz and Trimper in 2004. [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]

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]

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]

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]