Random Variables Research Articles

Factor-Analytic Variance-Covariance Structures for Prediction Into a Target Population of Environments.

Finlay-Wilkinson regression is a popular method for modeling genotype-environment interaction in plant breeding and crop variety testing. When environment is a random factor, this model may be cast as a factor-analytic variance-covariance structure, implying a regression on random latent environmental variables. This paper reviews such models with a focus on their use in the analysis of multi-environment trials for the purpose of making predictions in a target population of environments. We investigate the implication of random versus fixed effects assumptions, starting from basic analysis-of-variance models, then moving on to factor-analytic models and considering the transition to models involving observable environmental covariates, which promise to provide more accurate and targeted predictions than models with latent environmental variables.

A study on the small failure probabilities of cylindrical composite hydrogen storage tanks using subset simulation

Although composite hydrogen tanks are becoming increasingly intriguing, a detailed structural reliability analysis is still lacking. The current landscape of analysis for pressurised multilayer cylinders, while rich in research, lacks tools to deal with the low probabilities of failure that govern the design of hydrogen tanks. This study presents a computational framework integrating the Subset Simulation method (SS) for assessing the failure probability of composite tanks used for hydrogen storage. To explore how randomness impacts design parameters, this study utilises a limit state equation derived from the thin-walled circumferential model of composite pressure tanks. Five random variables, each with varying coefficients of variation (COVs), are incorporated into the analysis. For comparison and validation purposes, two methods Monte Carlo simulations and FORM have been used. The analysis revealed that SS excels at estimating the low failure probabilities of composite hydrogen tanks, and showed also the feasibility and accuracy of SS in the prediction of burst pressure since good agreement was obtained between the probabilistic approach and the experimental results. Furthermore, the uncertainties related to internal pressure and composite thickness affect significantly the reliability of the structure and can lead to the shrinkage of the safety margin and the failure of the vessel.

Bayesian credibility model with heavy tail random variables: calibration of the prior and application to natural disasters and cyber insurance

Bayesian credibility model with heavy tail random variables: calibration of the prior and application to natural disasters and cyber insurance

Minimizing distance between distribution functions: discrete counterparts to continuous random variables with applications in non-life insurance and stochastic reliability

In this work, we propose a novel family of procedures for deriving a discrete counterpart to a continuous probability distribution. They are based on a class of distances between cumulative distribution functions, including the Cramér, the Cramér-von Mises, and the Anderson-Darling distances as particular cases. The discrete counterpart is defined and derived as the random variable which minimizes its distance to the assigned continuous probability distribution among all the discrete random variables supported on the set of integers (or positive integers). Applications are provided with reference to the exponential and the normal distributions, among others; the discrete counterparts are derived, and their main properties are discussed, also in comparison with the one obtained through an existing discretization technique based on the preservation of the cumulative distribution function at integer values. Parameter estimation for these discrete analogs is discussed, along with an analysis of two real datasets, where they are compared in terms of goodness-of-fit with some popular discrete distributions. Furthermore, in order to highlight the effectiveness and the benefits derived from the proposed discretization procedures, we illustrate two practical applications in actuarial science and in reliability engineering. In the former case, the problem of determining the distribution of the total claims amount for a non-life insurance portfolio is considered, where the claim sizes can be modelled as iid random variables, and the number of claims is random as well. Actuaries use a recursive calculation method based on Panjer's formula, which requires an appropriate discretization of the individual claim distribution, and therefore the proposed procedures can be used. Since we consider two simple cases where the distribution of the total claims amount is analytically acquirable, the efficacy of the discretization procedures in the final approximation can be easily assessed and turns out to be satisfactory, especially when compared to the existing discretization. The latter case considers the determination of the reliability parameter for a complex stress-strength model. Here, the approximation by discretization is compared to Monte Carlo simulation and shown to be relevant: with a comparable if not smaller computational effort, discretization leads to similar results as simulation. Such discretizations can also naturally be applied to more complex problems such as scenario generation in stochastic programming. R code for this article is provided as supplementary material.

Chance-constrained programming for drinking water quality management under fuzziness and randomness

ABSTRACT In this paper, an inexact fuzzy random chance-constrained programming (IFRCCP) model was proposed to deal with the randomness and fuzziness in the optimization of booster cost for the water distribution system (WDS). The IFRCCP model was applied to a WDS to analyze the effects of randomness and fuzziness on the booster costs. The booster cost intervals were obtained under various violation levels and confidence levels. The results indicated that the lower and upper booster costs increased with the confidence levels of the lower limits and decreased with the violation levels of the lower limits for both normal and log-normal distribution fuzzy random variables (FRVs). Moreover, the increased magnitude of lower and upper booster costs under normal distribution FRV is a little less than that under log-normal distribution FRV, while the decreased magnitude of lower and upper booster costs under normal distribution FRV is larger than that under log-normal distribution FRV. The same regulation can be found for the FVR with both triangular and trapezoidal distribution FRVs. With the increase of booster number, the increased magnitude of the lower and upper booster costs decreased for both normal and log-normal distribution FRVs.

Deterministic modelling of implied volatility in cryptocurrency options with underlying multiple resolution momentum indicator and non-linear machine learning regression algorithm

AbstractModeling implied volatility (IV) is important for option pricing, hedging, and risk management. Previous studies of deterministic implied volatility functions (DIVFs) propose two parameters, moneyness and time to maturity, to estimate implied volatility. Recent DIVF models have included factors such as a moving average ratio and relative bid-ask spread but fail to enhance modeling accuracy. The current study offers a generalized DIVF model by including a momentum indicator for the underlying asset using a relative strength index (RSI) covering multiple time resolutions as a factor, as momentum is often used by investors and speculators in their trading decisions, and in contrast to volatility, RSI can distinguish between bull and bear markets. To the best of our knowledge, prior studies have not included RSI as a predictive factor in modeling IV. Instead of using a simple linear regression as in previous studies, we use a machine learning regression algorithm, namely random forest, to model a nonlinear IV. Previous studies apply DVIF modeling to options on traditional financial assets, such as stock and foreign exchange markets. Here, we study options on the largest cryptocurrency, Bitcoin, which poses greater modeling challenges due to its extreme volatility and the fact that it is not as well studied as traditional financial assets. Recent Bitcoin option chain data were collected from a leading cryptocurrency option exchange over a four-month period for model development and validation. Our dataset includes short-maturity options with expiry in less than six days, as well as a full range of moneyness, both of which are often excluded in existing studies as prices for options with these characteristics are often highly volatile and pose challenges to model building. Our in-sample and out-sample results indicate that including our proposed momentum indicator significantly enhances the model’s accuracy in pricing options. The nonlinear machine learning random forest algorithm also performed better than a simple linear regression. Compared to prevailing option pricing models that employ stochastic variables, our DIVF model does not include stochastic factors but exhibits reasonably good performance. It is also easy to compute due to the availability of real-time RSIs. Our findings indicate our enhanced DIVF model offers significant improvements and may be an excellent alternative to existing option pricing models that are primarily stochastic in nature.

Effect of cross-correlated hydraulic conductivity and compression index on nonlinear consolidation in randomly heterogeneous highly compressible aquitards

The problem of land subsidence due to groundwater pumping in highly compressible, randomly heterogenous aquitards with stress-dependent parameters is analyzed through one-dimensional Monte Carlo numerical simulations of nonlinear groundwater flow and consolidation. The natural logarithm of hydraulic conductivity (Y) and compression index (Cc) are considered spatially cross-correlated random variables. A stochastic simulation method based on a bivariate normal copula was applied to generate positive, negative, and uncorrelated realizations of the two random variables. The results show that when Y and Cc are correlated random parameters, the ensemble average total settlement is consistently larger (between 13% and 40% for the synthetic cases tested) than the total settlement obtained when the parameters are deterministic (perfectly known). In addition, the results of negative and no correlation between Y and Cc are similar in terms of the ensemble average and variance of total settlement, while positive correlation leads to larger values of total settlement and its variance. The stochastic approach employed here allows incorporating the uncertainty in the parameters in the simulation of the subsidence process, which is relevant for geotechnical engineering, design of structures and groundwater management.

Berry-Esseen bounds for self-normalized sums of locally dependent random variables

Berry-Esseen bounds for self-normalized sums of locally dependent random variables

Nonparametric statistical inference for compound models

This paper deals with the statistical inference in compound models, which are defined as a sum of i.i.d. random variables ξ 1 + ⋯ + ξ N , where the number of summands, N, is a random variable independent of ξ 1 , ξ 2 , … Using the novel technique based on the superposition of the Mellin and Laplace transforms, we construct a nonparametric estimator for the distribution of N, assuming that the distribution of ξ is known explicitly. Unlike most papers on this topic, we consider the general setting, where the distribution of N is not necessarily of Poisson type.

Fuzzy system reliability analysis based on new aging indexes

The concept of aging plays an important role in reliability analysis. The aim of this paper is providing the novel method to definition aging indexes based on fuzzy random variables and using the concept of α-pessimistic in both parametric and non-parametric approaches. In parametric approach, the concepts of survival function, hazard rate function and mean residual function were extended for fuzzy random variables. After that, we obtain and analyse these indexes for fuzzy exponential and fuzzy two-parameter Weibull distributions as two frequently used lifetime distribution in reliability theory. Moreover, with the assumption that the distribution of fuzzy observations is unknown (non-parametric approach), first an estimate for the fuzzy distribution function is presented, and then an estimate for the aging indices of the system is investigated. To do this, the concept of fuzzy empirical distribution function is investigated as an estimator of cumulative distribution function. Moreover, some properties of investigated estimator have been established.

Tilts, developmental modules, and cognitive differentiation-integration effort: A multi-study response to

Sorjonen et al. (2024) critique a recently published finding that cognitive tilts are heritable, which was advanced as a line of evidence supporting their substantive (rather than artefactual) nature. These researchers claim: i) that the heritability of tilts is simply a function of the heritabilities of the specific cognitive dimensions used in their estimation, and ii) that spuriously heritable tilts can be recovered using difference scores between psychometric, anthropometric, and even random number variables. Here, multiple studies employing three behavior genetic datasets are used to test these claims. Even when cognitive tilts are residualized for their association with their constituent abilities, they still exhibit small, but non-zero heritabilities. Shared environmentality (C) accounts for the largest proportion of variance among these residuals. Tilts generated using random numbers are, by contrast, in all cases associated with AE models, exhibiting near 100 % E variance, corresponding to error. In the Swedish Twin Registry, the tilt residual is positively correlated with a measure of life history speed (Mini-K score), suggesting that tilts capture cognitive differentiation-integration effort conditioned developmentally by C variance. Distinct latent factors among psychometric and anthropometric variables in the Georgia Twin Study are also found. These indicate the presence of distinct developmental modules, meaning that tilts estimated using manifest variables associated with different modules lack theoretical credibility, as also evidenced by weak cross loadings.

Fisher information bounds and applications to SDEs with small noise

In this paper, we first establish general bounds on the Fisher information distance to the class of normal distributions of Malliavin differentiable random variables. We then study the rate of Fisher information convergence in the central limit theorem for the solution of small noise stochastic differential equations and its additive functionals. We also show that the convergence rate is of optimal order.

Optimizing Distributions for Associated Entropic Vectors via Generative Convolutional Neural Networks.

The complete characterization of the almost-entropic region yields rate regions for network coding problems. However, this characterization is difficult and open. In this paper, we propose a novel algorithm to determine whether an arbitrary vector in the entropy space is entropic or not, by parameterizing and generating probability mass functions by neural networks. Given a target vector, the algorithm minimizes the normalized distance between the target vector and the generated entropic vector by training the neural network. The algorithm reveals the entropic nature of the target vector, and obtains the underlying distribution, accordingly. The proposed algorithm was further implemented with convolutional neural networks, which naturally fit the structure of joint probability mass functions, and accelerate the algorithm with GPUs. Empirical results demonstrate improved normalized distances and convergence performances compared with prior works. We also conducted optimizations of the Ingleton score and Ingleton violation index, where a new lower bound of the Ingleton violation index was obtained. An inner bound of the almost-entropic region with four random variables was constructed with the proposed method, presenting the current best inner bound measured by the volume ratio. The potential of a computer-aided approach to construct achievable schemes for network coding problems using the proposed method is discussed.

Event-triggered secure control for Markov jump neural networks with time-varying delays and subject to cyber-attacks via state estimation fuzzy approach

The investigation uses a state estimation fuzzy technique to address the problem of dynamic event-triggered secure control in Markov jump neural networks with time-varying delays subject to cyber-attacks. Two different deception attacks are given, each employing stochastic variables with a Bernoulli distribution. Specifically, this article presents a dynamic event-triggered strategy and energy restrictions to reduce network traffic and protect network resources during deception attacks. To prevent the system state from becoming unavailable, a state estimator is concurrently developed using the output signal. The application of Lyapunov stability theory yields sufficient criteria that ensure neural network stability. The study also accurately describes the controller gain's by solving Linear matrix inequality. Numerical examples are provided to demonstrate the theoretical results.

Robust sparse recovery with sparse Bernoulli matrices via expanders

Sparse binary matrices are of great interest in the field of sparse recovery, nonnegative compressed sensing, statistics in networks, and theoretical computer science. This class of matrices makes it possible to perform signal recovery with lower storage costs and faster decoding algorithms. In particular, Bernoulli (p) matrices formed by independent identically distributed (i.i.d.) Bernoulli (p) random variables are of practical relevance in the context of noise-blind recovery in nonnegative compressed sensing.In this work, we investigate the robust nullspace property of Bernoulli (p) matrices. Previous results in the literature establish that such matrices can accurately recover n-dimensional s-sparse vectors with m=O(sc(p)log⁡ens) measurements, where c(p)≤p is a constant dependent only on the parameter p. These results suggest that in the sparse regime, as p approaches zero, the (sparse) Bernoulli (p) matrix requires significantly more measurements than the minimal necessary, as achieved by standard isotropic subgaussian designs. However, we show that this is not the case.Our main result characterizes, for a wide range of sparsity levels s, the smallest p for which sparse recovery can be achieved with the minimal number of measurements. We also provide matching lower bounds to establish the optimality of our results and explore connections with the theory of invertibility of discrete random matrices and integer compressed sensing.

Reducing the coupling of metamaterial via random configuration

In this paper, we demonstrate the Anderson localization effect in coupled metamaterial structures. We introduce the random variables by randomly choosing the geometrical parameter of structures and randomly choosing the distance between structures to reduce the coupling of metamaterial and this decoupling effect is equivalent to Anderson localization effect, which can reduce the coupling without enlarging the area of unit cell. We demonstrate our idea by employing the experiments. Furthermore, we present an example of deflector to see how this decoupling effect can help us design functional devices.

Information geometry and alpha-parallel prior of the beta-logistic distribution

The hyperbolic secant distribution has several generalizations with applications in, for example, finance. In this study, we explore the dual geometric structure of one such generalization: the beta-logistic distribution. Within this family, two special cases of random variables, as examples, are of particular interests: their moments, by some recent results, give the Bernoulli and Euler polynomials, which are important objects in many areas of mathematics. This current study also uncovers that the beta-logistic distribution admits a α-parallel prior for any real number α, that has the potential for application in geometric statistical inference.

Addressing maximization bias in reinforcement learning with two-sample testing

Value-based reinforcement-learning algorithms have shown strong results in games, robotics, and other real-world applications. Overestimation bias is a known threat to those algorithms and can sometimes lead to dramatic performance decreases or even complete algorithmic failure. We frame the bias problem statistically and consider it an instance of estimating the maximum expected value (MEV) of a set of random variables. We propose the T-Estimator (TE) based on two-sample testing for the mean, that flexibly interpolates between over- and underestimation by adjusting the significance level of the underlying hypothesis tests. We also introduce a generalization, termed K-Estimator (KE), that obeys the same bias and variance bounds as the TE and relies on a nearly arbitrary kernel function. We introduce modifications of Q-Learning and the Bootstrapped Deep Q-Network (BDQN) using the TE and the KE, and prove convergence in the tabular setting. Furthermore, we propose an adaptive variant of the TE-based BDQN that dynamically adjusts the significance level to minimize the absolute estimation bias. All proposed estimators and algorithms are thoroughly tested and validated on diverse tasks and environments, illustrating the bias control and performance potential of the TE and KE.

Self-correlated spatial random variables: From an auto- to a sui- model respecification

This paper marks the 50-year publication anniversary of Besag's seminal spatial auto- models paper. His classic article synthesizes generic autoregressive specifications (i.e., a response variable appears on both sides of a regression equation and/or probability function equal sign) for the following six popular random variables: normal, logistic (i.e., Bernoulli), binomial, Poisson, exponential, and gamma. Besag dismisses these last two while recognizing failures of both as well as the more scientifically critical counts-oriented auto-Poisson. His initially unsuccessful subsequent work first attempted to repair them (e.g., pseudo-likelihood estimation), and then successfully revise them within the context of mixed models, formulating a spatially structured random effects term that effectively and efficiently absorbs and accounts for spatial autocorrelation in geospatial data. One remaining weakness of all but the auto-normal is a need to resort to Markov chain Monte Carlo (MCMC) techniques for legitimate estimation purposes. Recently, Griffith succeeded in devising an innovative uniform distribution genre—sui-uniform random variables—that accommodates spatial autocorrelation, too. Its most appealing feature is that, by applying two powerful mathematical statistical theorems (i.e., the probability integral transform, and the quantile function), it redeems Besag's auto- model failures. This paper details conversion of Besag's initial six modified variates, exemplifying them with both simulation experiments and publicly accessible real-world georeferenced data. The principal outcome is valuable spatial statistical advancements, with special reference to Moran eigenvector spatial filtering.

Shaping of the risk of a series-parallel manufacturing structure maintenance according to quasi-coherence and the [formula omitted]-th survival value

The paper presents the authors’ model for determining the probability value of the survival function of the difference of two random variables: TP – the amount of time of correct operation and TB – the amount of time of failure. For this purpose, the concept of K-th survival value is introduced. The K-th survival value defines the probability that the total time of correct operation of the production system will be longer by at least k time units (for k≥0) than the total amount of time of failures. The model was exemplified by a real production system with a series–parallel structure. In the nesting manufacturing structure, the availability of machines determines the number and the type of flow streams of the processed material. To formalise the chains of relations at a given Δt, this paper utilises the quasi-coherence property. The paper identifies four possible cases of system operation: 1) a fully operational system in which every machine is capable of meeting the assumed production schedule; 2) a system which has lost the property of quasi-coherence (certain system objects are in an inoperable state) but it is possible to meet the assumed production schedule; 3) a system which has lost the property of quasi-coherence but the assumed task schedule is possible to meet after redefining the material flow streams; 4) a system which has lost the property of quasi-coherence and it is impossible to meet the assumed production schedule. Based on the definition of the survival function [1] S of the random variable T: ST:=PT>τ=1-FTτ,τ∈R, the concept of K-th survival value was introduced. For possible cases, K-th survival value was defined as: KT1,Ti=PT1-Ti≥k=1-FT1-Tik (for i=2,3,4), where T1 and Ti are random variables with given probability distributions. In turn, k is a deterministic value that determines the total number of time units of correct system operation in relation to the total failure time. The application of the developed algorithm enables the system to be analysed in terms of three aspects: (1) to determine the probability of on-time execution of tasks, taking into account historical values of machine failure and correct operation durations; (2) to determine the stability of the system based on empirical data; (3) to monitor the level of risk in real time. The paper validates the model by determining the stability of the analysed system for real machine failure data. The introduced criterion of stochastic stability of the production system has been verified for data in which distributions of correct operation times and failure times are random variables from the family of Gamma distributions. The presented model can be included in the group of multifactorial risk assessment methods.