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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 maximal positive I I i I k i identifies the variables that co-vary the most in the population, whereas the minimal negative I I i I k i identifies synergistic clusters and the variables that differentiate-segregate the most in the population. Detailed state variables are reduced using the usual principle of maximum entropy (MaxEnt), whereas relaxation of the conjugate variables guarantees that the reduced equations are closed. Pursuing the work of Hu Kuo Ting and Te Sun Han, we show that information functions provide coordinates for binary variables and that they are analytically independent of the probability simplex for any set of finite variables. [Extracted from the article]

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]

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]

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]

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]

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, for a wide class of nonparametric regression models, new local linear kernel estimators are proposed that are uniformly consistent under close-to-minimal and visual conditions on design points. These estimators are universal in the sense that their designs can be either fixed and not necessarily satisfying the traditional regularity conditions, or random, while not necessarily consisting of independent or weakly dependent random variables. With regard to the design elements, only dense filling of the regression function domain with the design points without any specification of their correlation is assumed. This study extends the dense data methodology and main results of the authors' previous work for the case of regression functions of several variables. [ABSTRACT FROM AUTHOR]

For the RRT* algorithm, there are problems such as greater randomness, longer time consumption, more redundant nodes, and inability to perform local obstacle avoidance when encountering unknown obstacles in the path planning process of autonomous vehicles. And the artificial potential field method (APF) applied to autonomous vehicles is prone to problems such as local optimality, unreachable targets, and inapplicability to global scenarios. A fusion algorithm combining the improved RRT* algorithm and the improved artificial potential field method is proposed. First of all, for the RRT* algorithm, the concept of the artificial potential field and probability sampling optimization strategy are introduced, and the adaptive step size is designed according to the road curvature. The path post-processing of the planned global path is carried out to reduce the redundant nodes of the generated path, enhance the purpose of sampling, solve the problem where oscillation may occur when expanding near the target point, reduce the randomness of RRT* node sampling, and improve the efficiency of path generation. Secondly, for the artificial potential field method, by designing obstacle avoidance constraints, adding a road boundary repulsion potential field, and optimizing the repulsion function and safety ellipse, the problem of unreachable targets can be solved, unnecessary steering in the path can be reduced, and the safety of the planned path can be improved. In the face of U-shaped obstacles, virtual gravity points are generated to solve the local minimum problem and improve the passing performance of the obstacles. Finally, the fusion algorithm, which combines the improved RRT* algorithm and the improved artificial potential field method, is designed. The former first plans the global path, extracts the path node as the temporary target point of the latter, guides the vehicle to drive, and avoids local obstacles through the improved artificial potential field method when encountered with unknown obstacles, and then smooths the path planned by the fusion algorithm, making the path satisfy the vehicle kinematic constraints. The simulation results in the different road scenes show that the method proposed in this paper can quickly plan a smooth path that is more stable, more accurate, and suitable for vehicle driving. [ABSTRACT FROM AUTHOR]

Expected utility theory is critical for modeling rational decision making under uncertainty, guiding economic agents as they seek to optimize outcomes. Traditional methods often require restrictive assumptions about underlying stochastic processes, limiting their applicability. This paper expands the theoretical framework by considering investment returns modeled by a stochastically ordered family of random variables under the convolution order, including Poisson, Gamma, and exponential distributions. Utilizing fractional calculus, we derive explicit, closed-form expressions for the derivatives of expected utility for various utility functions, significantly broadening the potential for analytical and computational applications. We apply these theoretical advancements to a case study involving the optimal production strategies of competitive firms, demonstrating the practical implications of our findings in economic decision making. [ABSTRACT FROM AUTHOR]

Monitoring the ratio of two correlated normal random variables is often used in many industrial manufacturing processes. At the same time, measurement errors inevitably exist in most processes, which have different effects on the performance of various charting schemes. This paper comprehensively analyses the impacts of measurement errors on the detection ability of the cumulative sum (CUSUM) charting schemes for the ratio of two correlated normal variables. A thorough numerical assessment is performed using the Monte Carlo simulation, and the results indicate that the measurement errors negatively impact the performance of the CUSUM scheme for the ratio of two correlated normal variables. Increasing the number of measurements per set is not a lucrative approach for minimizing the negative impact of measurement errors on the performance of the CUSUM charting scheme when monitoring the ratio of two correlated normal variables. We consider a food formulation as an example that illustrates the quality control problems involving the ratio of two correlated normal variables in an industry with a measurement error. The results are presented, along with some suggestions for further study. [ABSTRACT FROM AUTHOR]

This paper investigates the randomly stopped sums, minima and maxima of heavy- and light-tailed random variables. The conditions on the primary random variables, which are independent but generally not identically distributed, and counting random variable are given in order that the randomly stopped sum, random minimum and maximum is heavy/light tailed. The results generalize some existing ones in the literature. The examples illustrating the results are provided. [ABSTRACT FROM AUTHOR]

This paper describes various selected properties and features of negative binomial (NB) random variables, with special reference to NB2 (i.e., p = 2), and some generalizations to NBp (i.e., p ≥ 2), specifications. It presents new results (e.g., the NBp moment-generating function) with regard to the relationship between a sample mean and its accompanying variance, as well as spatial statistical/econometric numerical and empirical examples, whose parameter estimators are maximum likelihood or method of moment ones. Finally, it highlights the Moran eigenvector spatial filtering methodology within the context of generalized linear modeling, demonstrating it in terms of spatial negative binomial regression. Its overall conclusion is a bolstering of important findings the literature already reports with a newly recognized empirical example of an NB3 phenomenon. [ABSTRACT FROM AUTHOR]

We develop a framework for creating distortion functions that are used to construct new bivariate copulas. It is achieved by transforming non-negative random variables with Lomax-related distributions. In this paper, we apply the distortions to the base copulas of independence, Clayton, Frank, and Gumbel copulas. The properties of the tail dependence coefficient, tail order, and concordance ordering are explored for the new families of distorted copulas. We conducted an empirical study using the daily net returns of Amazon and Google stocks from January 2014 to December 2023. We compared the popular Clayton, Gumbel, Frank, and Gaussian copula models to their corresponding distorted copula models induced by the unit-Lomax and unit-inverse Pareto distortions. The new families of distortion copulas are equipped with additional parameters inherent in the distortion function, providing more flexibility, and are demonstrated to perform better than the base copulas. After analyzing the data, we have found that the joint extremes of Amazon and Google stocks are more likely for high daily net returns than for low daily net returns. [ABSTRACT FROM AUTHOR]

The accurate prediction of short-term platform motions in a real environment is crucial for the safe design, operation, and maintenance of floating offshore wind turbines (FOWTs). Numerical simulations of motions are typically associated with high uncertainties due to abstracted theoretical models, empirical parameters, initial environment parameters, etc. Therefore, it is necessary to integrate other sources of information associated with less uncertainty, e.g., monitoring data, for accurate predictions. In this paper, we propose a probabilistic prediction based on the Bayesian approach that logically integrates motion monitoring data with simulated motion predictions of FOWTs, considering uncertainties in the environment model, structural properties, motion prediction method, monitoring data, etc. The approach consists of constructing a prior probability density function (PDF) of a random variable (which characterizes the largest value of the initial motion response) via numerical simulations and a likelihood function based on platform motion monitoring data and deriving a posterior PDF of the random variable by Bayesian updating. Then, posterior distributions of short-term extreme motion responses are derived using the posterior PDF of the random variable, representing lower uncertainty and improved accuracy. A Metropolis–Hastings algorithm is adopted to obtain PDFs of complex probability distributions. The effectiveness of the approach is demonstrated on a real FOWT platform in Scotland. The proposed probabilistic prediction approach results in posterior distributions of short-term extreme platform motions associated with less uncertainty and higher accuracy, which is attributed to integrating prior knowledge with monitoring data. [ABSTRACT FROM AUTHOR]

The well-known inspection paradox or waiting time paradox states that, in a renewal process, the inspection interval is stochastically larger than a common interarrival time having a distribution function F, where the inspection interval is given by the particular interarrival time containing the specified time point of process inspection. The inspection paradox may also be expressed in terms of expectations, where the order is strict, in general. A renewal process can be utilized to describe the arrivals of vehicles, customers, or claims, for example. As the inspection time may also be considered a random variable T with a left-continuous distribution function G independent of the renewal process, the question arises as to whether the inspection paradox inevitably occurs in this general situation, apart from in some marginal cases with respect to F and G. For a random inspection time T, it is seen that non-trivial choices lead to non-occurrence of the paradox. In this paper, a complete characterization of the non-occurrence of the inspection paradox is given with respect to G. Several examples and related assertions are shown, including the deterministic time situation. [ABSTRACT FROM AUTHOR]

In this paper, under some suitable assumptions, using the Taylor expansion, Borel–Cantelli lemma and the almost sure central limit theorem for independent random variables, the almost sure central limit theorem for error variance estimator in the pth-order nonlinear autoregressive processes with independent and identical distributed errors was established. Four examples, first-order autoregressive processes, self-exciting threshold autoregressive processes, threshold-exponential AR progresses and multilayer perceptrons progress, are given to verify the results. [ABSTRACT FROM AUTHOR]

Computational statistics is a critical skill for professionals in fields such as data science, statistics, and related disciplines. One essential aspect of computational statistics is the ability to simulate random variables from specified probability distributions. Commonly employed techniques for sampling random variables include the inverse transform method, acceptance–rejection method, and Box–Muller transformation, all of which rely on sampling from the uniform (0 , 1) distribution. A significant concept in statistics is the finite mixture model, characterized by a convex combination of multiple probability density functions. In this paper, we introduce a modified version of the composition method, a standard approach for sampling finite mixture models. Our modification offers the advantage of relying on sampling from the uniform (0 , 1) distribution, aligning with prevalent methods in computational statistics. This alignment simplifies teaching computational statistics courses, as well as having other benefits. We offer several examples to illustrate the approach. [ABSTRACT FROM AUTHOR]

In general, the extended Kalman filter (EKF) has a wide range of applications, aiming to minimize symmetric loss function (mean square error) and improve the accuracy and efficiency of state estimation. As the nonlinear model complexity increases, rounding errors gradually amplify, leading to performance degradation. After multiple iterations, divergence may occur. The traditional extended Kalman filter cannot accurately estimate the nonlinear model, and these errors still have an impact on the accuracy. To improve the filtering performance of the extended Kalman filter (EKF), this paper proposes a new extended Kalman filter (REKF) method that utilizes the statistical properties of the rounding error to enhance the estimation accuracy. After establishing the state model and measurement model, the residual term is used to replace the higher-order term in the Taylor expansion, and the least squares method is applied to identify the residual term step by step. Then, the iterative process of updating the extended Kalman filter is carried out. Within the Kalman filter framework, a higher-order rounding error-based extended Kalman filter (REKF) is designed for the joint estimation of rounding error and random variables, and the solution method for the rounding error is considered for the multilevel approximation of the original function. Through numerical simulations on a general nonlinear model, the higher-order rounding error-based extended Kalman filter (REKF) achieves better estimation results than the extended Kalman filter (EKF) and improves the filtering accuracy by utilizing the higher-order rounding error information, which also proves the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we consider a tandem dual queuing system consisting of multi-server stages. Stage 1 is characterized by an infinite buffer, one-by-one service of customers, and an exponential distribution of service times. Stage 2 is characterized by a finite buffer and a phase-type distribution of service times. Service at Stage 2 is provided to groups of customers. The service time of a group depends on the size of the group. The size is restricted by two thresholds. The waiting time of a customer at each stage is limited by a random variable with an exponential distribution, with the parameter depending on the stage. After service at Stage 1, a customer can depart from the system or try to enter Stage 2. If the buffer at this stage is full, the customer is either lost or returns for service at Stage 1. Customer arrivals are described by the versatile Markov arrival process. The system is studied via consideration of a multi-dimensional continuous-time Markov chain. Numerical examples, which highlight the influence of the thresholds on the system performance measures, are presented. The possibility of solving optimization problems is illustrated. [ABSTRACT FROM AUTHOR]

The main focus of this paper is the derivation of the structural properties of the test channels of Wyner's operational information rate distortion function (RDF), R ¯ (Δ X) , for arbitrary abstract sources and, subsequently, the derivation of additional properties for a tuple of multivariate correlated, jointly independent, and identically distributed Gaussian random variables, { X t , Y t } t = 1 ∞ , X t : Ω → R n x , Y t : Ω → R n y , with average mean-square error at the decoder and the side information, { Y t } t = 1 ∞ , available only at the decoder. For the tuple of multivariate correlated Gaussian sources, we construct optimal test channel realizations which achieve the informational RDF, R ¯ (Δ X) = ▵ inf M (Δ X) I (X ; Z | Y) , where M (Δ X) is the set of auxiliary RVs Z such that P Z | X , Y = P Z | X , X ^ = f (Y , Z) , and E { | | X − X ^ | | 2 } ≤ Δ X . We show the following fundamental structural properties: (1) Optimal test channel realizations that achieve the RDF and satisfy conditional independence, P X | X ^ , Y , Z = P X | X ^ , Y = P X | X ^ , E X | X ^ , Y , Z = E X | X ^ = X ^. (2) Similarly, for the conditional RDF, R X | Y (Δ X) , when the side information is available to both the encoder and the decoder, we show the equality R ¯ (Δ X) = R X | Y (Δ X) . (3) We derive the water-filling solution for R X | Y (Δ X) . [ABSTRACT FROM AUTHOR]

The partial information decomposition (PID) framework is concerned with decomposing the information that a set of (two or more) random variables (the sources) has about another variable (the target) into three types of information: unique, redundant, and synergistic. Classical information theory alone does not provide a unique way to decompose information in this manner and additional assumptions have to be made. One often overlooked way to achieve this decomposition is using a so-called measure of union information—which quantifies the information that is present in at least one of the sources—from which a synergy measure stems. In this paper, we introduce a new measure of union information based on adopting a communication channel perspective, compare it with existing measures, and study some of its properties. We also include a comprehensive critical review of characterizations of union information and synergy measures that have been proposed in the literature. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to implement a simulation model in @RISKTM and study the impact of incorporating random variables, such as the degree days in a traditional deterministic model, for calculating the optimum thickness of thermal insulation in walls. Currently, green buildings have become important because of the increasing worldwide interest in the reduction of environmental pollution. One method of saving energy is to use thermal insulation. The optimum thickness of these insulators has traditionally been calculated using deterministic models. With the information generated from real data using the degree days required in a certain zone in Palestine during winter, random samples of the degree days required annually in this town were generated for periods of 10, 20, 50, and 70 years. The results showed that the probability of exceeding the net present value of the cost calculated using deterministic analysis ranges from 0% to 100%, without regard to the inflation rate. The results also show that, for design lifetimes greater than 40 years, the risk of overspending is lower if the building lasts longer than the period for which it was designed. Moreover, this risk is transferred to whomever will pay the operating costs of heating the building. The contribution of this research is twofold: (a) a stochastic approach is incorporated into the traditional models that determine the optimum thickness of thermal insulation used in buildings, by introducing the variability of the degree days required in a given region; (b) a measure of the economic risk incurred by building heating is established as a function of the years of use for which the building is designed and the number of years it is actually used. [ABSTRACT FROM AUTHOR]

For decades, conventional wisdom maintained that binary 0–1 Bernoulli random variables cannot contain extra-binomial variation. Taking an unorthodox stance, Hilbe actively disagreed, especially for correlated observation instances, arguing that the universally adopted diagnostic Pearson or deviance dispersion statistics are insensitive to a variance anomaly in a binary context, and hence simply fail to detect it. However, having the intuition and insight to sense the existence of this departure from standard mathematical statistical theory, but being unable to effectively isolate it, he classified this particular over-/under-dispersion phenomenon as implicit. This paper explicitly exposes his hidden quantity by demonstrating that the variance in/deflation it represents occurs in an underlying predicted beta random variable whose real number values are rounded to their nearest integers to convert to a Bernoulli random variable, with this discretization masking any materialized extra-Bernoulli variation. In doing so, asymptotics linking the beta-binomial and Bernoulli distributions show another conventional wisdom misconception, namely a mislabeling substitution involving the quasi-Bernoulli random variable; this undeniably is not a quasi-likelihood situation. A public bell pepper disease dataset exhibiting conspicuous spatial autocorrelation furnishes empirical examples illustrating various features of this advocated proposition. [ABSTRACT FROM AUTHOR]

In reliability studies, we are interested in the behaviour of a system when it interacts with its surrounding environment. To assess the system's behaviour in a reliability sense, we can take the system's intrinsic quality as strength and the outcome of interactions as stress. Failure is observed whenever stress exceeds strength. Taking Y as a random variable representing the stress the system experiences and random variable X as its strength, the probability of not failing can be taken as a proxy for the reliability of the component and given as P (Y < X) = 1 − P (X < Y) . This way, in the present paper, it is considered that X and Y follow generalized extreme value distributions, which represent a family of continuous probability distributions that have been extensively applied in engineering and economic contexts. Our contribution deals with a more general scenario where stress and strength are not independent and copulas are used to model the dependence between the involved random variables. In such modelling framework, we explored the proper selection of copula models characterizing the dependence structure. The Gumbel–Hougaard, Frank, and Clayton copulas were used for modelling bivariate data sets. In each case, information criteria were considered to compare the modelling capabilities of each copula. Two economic applications, as well as an engineering one, on real data sets are discussed. Overall, an easy-to-use methodological framework is described, allowing practitioners to apply it to their own research projects. [ABSTRACT FROM AUTHOR]

In this paper, we investigate two types of the conditional strong law of large numbers with a new notion of conditionally independent random variables under G-expectation which are related to the symmetry G-function. Our limit theorem demonstrates that the cluster points of empirical averages fall within the bounds of the lower and upper conditional expectations with lower probability one. Moreover, for conditionally independent random variables with identical conditional distributions, we show the existence of two cluster points of empirical averages that correspond to the essential minimum and essential maximum expectations, respectively, with G-capacity one. [ABSTRACT FROM AUTHOR]

Obtaining wind energy for the production of electric energy plays a key role in overcoming the problems associated with climate change and the dwindling reserves of traditional types of energy resources. The purpose of this work is to analyze current methods of energy estimation and forecasting, to consider the main classifications of forecasts and methods used in their construction and to review the main types of mathematical distributions used to calculate the speed and power of wind flow, depending on specific geographical conditions. In recent years, there has been an increase in the capacity of modern wind generators, which has significantly improved the efficiency of wind energy parks. The initial stage in determining the feasibility of involving a particular energy source in the overall energy system of the region is a preliminary assessment of the energy potential, allowing one to determine the possible percentage of substitution of traditional energy. To solve such a problem, it is necessary to use models of energy supply. Evaluation of wind as a resource creates certain difficulties in modeling because this resource is stochastic and variable. In this regard, this paper proposes to consider various models for estimating wind energy potential, which can be classified into empirical models and models based on the application of modern intelligent data analysis technologies. The paper presents an analysis of the existing models for estimating the amount of energy, which can be used in a system designed to determine the most optimal configuration of the energy system based on the use of different conversion technologies most relevant to the case under study, and it also serves as the basis for creating digital twins designed to model and optimize the operation of the projected energy complex. [ABSTRACT FROM AUTHOR]

In this paper, we provide geometric insights with visualization into the multivariate Gaussian distribution and its entropy and mutual information. In order to develop the multivariate Gaussian distribution with entropy and mutual information, several significant methodologies are presented through the discussion, supported by illustrations, both technically and statistically. The paper examines broad measurements of structure for the Gaussian distributions, which show that they can be described in terms of the information theory between the given covariance matrix and correlated random variables (in terms of relative entropy). The content obtained allows readers to better perceive concepts, comprehend techniques, and properly execute software programs for future study on the topic's science and implementations. It also helps readers grasp the themes' fundamental concepts to study the application of multivariate sets of data in Gaussian distribution. The simulation results also convey the behavior of different elliptical interpretations based on the multivariate Gaussian distribution with entropy for real-world applications in our daily lives, including information coding, nonlinear signal detection, etc. Involving the relative entropy and mutual information as well as the potential correlated covariance analysis, a wide range of information is addressed, including basic application concerns as well as clinical diagnostics to detect the multi-disease effects. [ABSTRACT FROM AUTHOR]

This work examines the asymptotic characteristics of a conditional set-indexed empirical process composed of functional ergodic random variables with missing at random (MAR). This paper's findings enlarge the previous advancements in functional data analysis through the use of empirical process methodologies. These results are shown under specific structural hypotheses regarding entropy and under appealing situations regarding the model. The regression operator's asymptotic (1 − α) -confidence interval is provided for 0 < α < 1 as an application. Additionally, we offer a classification example to demonstrate the practical importance of the methodology. [ABSTRACT FROM AUTHOR]

Dependent random variables play a crucial role in various fields, from finance and statistics to engineering and environmental sciences. Often, interest lies in understanding the aggregate sum of a collection of dependent variables with random weights. In this paper, we provide a comprehensive study of the distribution of the aggregate sum with random weights. Expressions derived include those for the cumulative distribution function, probability density function, conditional expectation, moment generating function, characteristic function, cumulant generating function, moments, variance, skewness, kurtosis, cumulants, value at risk and the expected shortfall. Real data applications are discussed. [ABSTRACT FROM AUTHOR]

Identifying the optimal cabin layout is an important way to improve the efficiency of ship systems and ensure the efficient circulation of personnel and materials. The ship task state refers to the state maintained by the joint actions of ship machinery and equipment, cargo, and personnel when facing different jobs and tasks during operation. A cabin layout that facilitates multitasking states can improve the efficiency of collaboration between systems and ensure the operation of the ship. The demand for human flow and logistics is different in multitasking states. To express the demand in mathematical form, there is a certain random uncertainty in the numerical quantification of the demand. Thus, to better meet the needs of different states, the coefficient values of each state can be integrated using special methods. Ensuring values' initial preference to the greatest extent inevitably produces a degree of cognitive uncertainty. Therefore, uncertainty analysis is necessary for cabin layout design to be used for multitasking states. In this paper, a deterministic optimization platform of cabin layout in multitasking states is obtained. Adjacent and circulating strength coefficients are obtained through numerical quantization of the demand for human flow and logistics. The random uncertainty in the input values of two coefficients was represented by random variables, and the cognitive uncertainty was represented by interval variables. In order to solve the problem of two types of variables, a random-interval hybrid uncertainty model was established. Through random intervalization and interval randomization, three cases, of random variables, interval variables, and random variables and interval variables, were studied. The probability distribution of the model function was used to evaluate the influence of different compositions of uncertainty parameters on the robustness of the cabin layout scheme. The necessity and effectiveness of uncertainty analysis in multitasking cabin layout are discussed below. [ABSTRACT FROM AUTHOR]

The fast generation of values of the beta random variable is a subject of great interest and multiple applications, ranging from purely mathematical and statistical ones to applications in management and production, among others. There are several methods for generating these values, with one of the essential points for their design being the selection of random seeds. Two interesting aspects converge here: the use of sequences as inputs (and the need for them to verify properties such as randomness and uniformity, which are verified through statistical test suites) and the design of the algorithm for the generation of the variable. In this paper, we analyse, in detail, the algorithms that have been developed in the literature, both from a mathematical/statistical and computational point of view. We also provide empirical development using R software, which is currently in high demand and is one of the main novelties with respect to previous comparisons carried out in FORTRAN. We establish which algorithms are more efficient and in which contexts, depending on the different values of the parameters, allowing the user to determine the best method given the experimental conditions. [ABSTRACT FROM AUTHOR]

In response to the growing demand for economic and social development, there has been a significant increase in the integration of distributed generation (DG) into distribution networks. This paper proposes a dynamic risk assessment method for voltage violations in distribution networks with DG. Firstly, considering the characteristics of random variables such as load and DG, a probability density function estimation method based on boundary kernel density estimation is proposed. This method accurately models the probability of random variables under different time and external environmental conditions, such as wind speed and global horizontal radiation. Secondly, to address the issue of correlated DG in the same region, an independent transformation method based on the Rosenblatt inverse transform is proposed, which enhances the accuracy of probabilistic load flow. Thirdly, a voltage violation severity index based on the utility function is proposed. This index, in combination with probabilistic load flow results, facilitates the quantitative assessment of voltage violation risks. Finally, the accuracy of the proposed method is verified on the IEEE-33 system. [ABSTRACT FROM AUTHOR]

The selection of an appropriate development methodology is a critical strategic decision when managing a New Product Development (NPD) project. However, accurately estimating project duration based on the chosen methodology remains a challenge. This paper addresses the limitations of existing models and proposes a novel NPD project model that allows for testing and evaluation of different product development strategies. The model considers Waterfall, Spiral, Agile, and Hybrid methodologies and provides system engineers and project managers with decision-making tools to determine the optimal strategy and understand associated tradeoffs. The model is validated using real projects from various organizations and methodologies. It incorporates stochastic variables, risk management, and dynamic resource allocation, while addressing both Waterfall and Agile methodologies. The study contributes to the body of knowledge by offering practical tools for system engineers and project managers for choosing development methodology, improving project duration estimation, and identifying critical processes and risks in NPD projects. The research results also provide a basis for further studies and can benefit researchers interested in systems engineering methodologies. The proposed model fills a gap in the literature by providing a validated NPD model to evaluate the impact of different product development methodologies on project duration. [ABSTRACT FROM AUTHOR]

Monte Carlo simulation is performed with uniformly distributed U(0,1) pseudo-random numbers. Because the numbers are generated from a mathematical formula, they will contain some serial correlation, even if very small. This serial correlation becomes embedded in the correlation structure of the response variable. The response variable becomes an asynchronous time series. This leads to hidden errors in the response variable. The purpose of this paper is to illustrate how this happens and how it can be corrected. The method is demonstrated for the case of a simple queue for which the time in the system is known exactly from theory. The paper derives the correlation between an exponential random variable and its antithetic counterpart obtained by power transform with an infinitesimal negative exponent. [ABSTRACT FROM AUTHOR]

The optimization of the sampling scheme is particularly important in order to achieve sustainability in quality management. This paper discusses the problem of optimizing the design of metrological sampling scheme when the mean is a random variable. Assuming that the prior distribution of product means is known, a Bayesian posterior probability is calculated by using the likelihood function with decision variables to measure the sampling risk, and the expected cost of the sampling scheme is calculated based on the protection of producer and user risk in combination with the Taguchi quality loss function. The influence of model parameters on the selection of the optimal sampling scheme is investigated through sensitivity analysis. The model constructed in this paper solves the problem of sampling design in the case of food processing enterprises, quantifies the quality loss of products in the sampling process, facilitates sustainable quality management of enterprises, and has important theoretical significance and application value for sustainable business management of food processing enterprises. [ABSTRACT FROM AUTHOR]

This paper focuses mainly on the problem of computing the γ th , γ > 0 , moment of a random variable Y n : = ∑ i = 1 n α i X i in which the α i 's are positive real numbers and the X i 's are independent and distributed according to noncentral chi-square distributions. Finding an analytical approach for solving such a problem has remained a challenge due to the lack of understanding of the probability distribution of Y n , especially when not all α i 's are equal. We analytically solve this problem by showing that the γ th moment of Y n can be expressed in terms of generalized hypergeometric functions. Additionally, we extend our result to computing the γ th moment of Y n when X i is a combination of statistically independent Z i 2 and G i in which the Z i 's are distributed according to normal or Maxwell–Boltzmann distributions and the G i 's are distributed according to gamma, Erlang, or exponential distributions. Our paper has an immediate application in interest rate modeling, where we can explicitly provide the exact transition probability density function of the extended Cox–Ingersoll–Ross (ECIR) process with time-varying dimension as well as the corresponding γ th conditional moment. Finally, we conduct Monte Carlo simulations to demonstrate the accuracy and efficiency of our explicit formulas through several numerical tests. [ABSTRACT FROM AUTHOR]

The increasing penetration rate of electric vehicles, associated with a growing charging demand, could induce a negative impact on the electric grid, such as higher peak power demand. To support the electric grid, and to anticipate those peaks, a growing interest exists for forecasting the day-ahead charging demand of electric vehicles. This paper proposes the enhancement of a state-of-the-art deep neural network to forecast the day-ahead charging demand of electric vehicles with a time resolution of 15 min. In particular, new features have been added on the neural network in order to improve the forecasting. The forecaster is applied on an important use case of a local charging site of a hospital. The results show that the mean-absolute error (MAE) and root-meansquare error (RMSE) are respectively reduced by 28.8% and 19.22% thanks to the use of calendar and weather features. The main achievement of this research is the possibility to forecast a high stochastic aggregated EV charging demand on a day-ahead horizon with a MAE lower than 1 kW. [ABSTRACT FROM AUTHOR]

In this paper, we study a distributionally robust optimization (DRO) problem with affine decision rules. In particular, we construct an ambiguity set based on a new family of Wasserstein metrics, shortfall–Wasserstein metrics, which apply normalized utility-based shortfall risk measures to summarize the transportation cost random variables. In this paper, we demonstrate that the multi-dimensional shortfall–Wasserstein ball can be affinely projected onto a one-dimensional one. A noteworthy result of this reformulation is that our program benefits from finite sample guarantee without a dependence on the dimension of the nominal distribution. This distributionally robust optimization problem also has computational tractability, and we provide a dual formulation and verify the strong duality that enables a direct and concise reformulation of this problem. Our results offer a new DRO framework that can be applied in numerous contexts such as regression and portfolio optimization. [ABSTRACT FROM AUTHOR]

In this paper, we extend the Lomax–Rayleigh distribution to increase its kurtosis. The construction of this distribution is based on the idea of the Slash distribution, that is, its representation is based on the quotient of two independent random variables, one being a random variable with a Lomax–Rayleigh distribution and the other a beta (q , 1) . Based on the representation of this family, we study its basic properties, such as moments, coefficients of skewness, and kurtosis. We perform statistical inference using the methods of moments and maximum likelihood. To illustrate this methodology, we apply it to two real data sets. [ABSTRACT FROM AUTHOR]

In this paper, we present a new method to construct new classes of distortion functions. A distortion function maps the unit interval to the unit interval and has the characteristics of a cumulative distribution function. The method is based on the transformation of an existing non-negative random variable whose distribution function, named the generating distribution, may contain more than one parameter. The coherency of the resulting risk measures is ensured by restricting the parameter space on which the distortion function is concave. We studied cases when the generating distributions are exponentiated exponential and Gompertz distributions. Closed-form expressions for risk measures were derived for uniform, exponential, and Lomax losses. Numerical and graphical results are presented to examine the effects of the parameter values on the risk measures. We then propose a simple plug-in estimate of risk measures and conduct simulation studies to compare and demonstrate the performance of the proposed estimates. The plug-in estimates appear to perform slightly better than the well-known L-estimates, but also suffer from biases when applied to heavy-tailed losses. [ABSTRACT FROM AUTHOR]

Benchmarking different optimization algorithms is tasky, particularly for network-based cellular communication systems. The design and management process of these systems involves many stochastic variables and complex design parameters that demand an unbiased estimation and analysis. Though several optimization algorithms exist for different parametric modeling and tuning, an in-depth evaluation of their functional performance has not been adequately addressed, especially for cellular communication systems. Firstly, in this paper, nine key numerical and global optimization algorithms, comprising Gauss–Newton (GN), gradient descent (GD), Genetic Algorithm (GA), Levenberg–Marguardt (LM), Quasi-Newton (QN), Trust-Region–Dog-Leg (TR), pattern search (PAS), Simulated Annealing (SA), and particle swam (PS), have been benchmarked against measured data. The experimental data were taken from different radio signal propagation terrains around four eNodeB cells. In order to assist the radio frequency (RF) engineer in selecting the most suitable optimization method for the parametric model tuning, three-fold benchmarking criteria comprising the Accuracy Profile Benchmark (APB), Function Evaluation Benchmark (FEB), and Execution Speed Benchmark (ESB) were employed. The APB and FEB were quantitatively compared against the measured data for fair benchmarking. By leveraging the APB performance criteria, the QN achieved the best results with the preferred values of 98.34, 97.31, 97.44, and 96.65% in locations 1–4. The GD attained the worst performance with the lowest APE values of 98.25, 95.45, 96.10, and 95.70 in the tested locations. In terms of objective function values and their evaluation count, the QN algorithm shows the fewest function counts of 44, 44, 56, and 44, and the lowest objective values of 80.85, 37.77, 54.69, and 41.24, thus attaining the best optimization algorithm results across the study locations. The worst performance was attained by the GD with objective values of 86.45, 39.58, 76.66, and 54.27, respectively. Though the objective values achieved with global optimization methods, PAS, GA, PS, and SA, are relatively small compared to the QN, their function evaluation counts are high. The PAS, GA, PS, and SA recorded 1367, 2550, 3450, and 2818 function evaluation counts, which are relatively high. Overall, the QN algorithm achieves the best optimization, and it can serve as a reference for RF engineers in selecting suitable optimization methods for propagation modeling and parametric tuning. [ABSTRACT FROM AUTHOR]

In this paper, by establishing a Bernstein inequality for m-asymptotically almost negatively associated random variables, some results on consistency for the nearest neighbor estimator of the density function are further established. The results generalize some existing ones in the literature. Some numerical simulations are also provided to support the results. [ABSTRACT FROM AUTHOR]

From the perspective of wireless communication, as communication systems become more complex, order statistics have gained increasing importance, particularly in evaluating the performance of advanced technologies in fading channels. However, existing analytical methods are often too complex for practical use. In this research paper, we introduce innovative statistical findings concerning the sum of ordered gamma-distributed random variables. We examine various channel scenarios where these variables are independent but not-identically distributed. To demonstrate the practical applicability of our results, we provide a comprehensive closed-form expression for the statistics of the signal-to-interference-plus-noise ratio in a multiuser scheduling system. We also present numerical examples to illustrate the effectiveness of our approach. To ensure the accuracy of our analysis, we validate our analytical results through Monte Carlo simulations. [ABSTRACT FROM AUTHOR]

The conventional optimal power flow (OPF) is confronted with challenges in tackling more than three objectives and the stochastic characteristics due to the uncertainty and intermittence of the RESs. However, there are few methods available that simultaneously address high-dimensional objective optimization and uncertainty handling. This paper proposes a set-based group search optimizer (SetGSO) to tackle the stochastic many-objective optimal power flow (MaOPF) of power systems penetrated with renewable energy sources. The proposed SetGSO depicts the original stochastic variables by set-based individuals under the evolutionary strategy of the basic GSO, without using repeated sampling or probabilistic information. Consequently, two metrics, hyper-volume and average imprecision, are introduced to transform the stochastic MaOPF into a deterministic bi-objective OPF, guaranteeing a much superior Pareto-optimal front. Finally, our method was evaluated on three modified bus systems containing renewable energy sources, and compared with the basic GSO using Monte Carlo sampling (GSO-MC) and a set-based genetic algorithm (SetGA) in solving the stochastic MaOPF. The numerical results demonstrate a saving of 90% of the computation time in the proposed SetGSO method compared to sampling-based approaches and it achieves improvements in both the hyper-volume and average imprecision indicators, with a maximum enhancement of approximately 30% and 7% compared to SetGA. [ABSTRACT FROM AUTHOR]

This paper studies a linear regression model in which the errors are asymptotically almost negatively associated (AANA, in short) random variables. Firstly, the central limit theorem for AANA sequences of random variables is established. Then, we use the central limit theorem to investigate the asymptotic normality of the M-estimator for the unknown parameters. Some results for independent and negatively associated (NA, in short) random variables are extended to the case of AANA setting. Finally, a simulation is carried out to verify the asymptotic normality of the M-estimator in the model. [ABSTRACT FROM AUTHOR]