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This document is a letter to the editor addressing a typographical error in the formulas for the double Pareto-lognormal distribution and the normal-Laplace distribution. The authors clarify that the formulas themselves are correct, but there was an error in the expression of the Mills ratio in the correction by Amini and Rabbani. The authors provide the correct formulas for both distributions and offer further explanation upon request. The authors are affiliated with Juraj Dobrila University of Pula in Croatia. [Extracted from the article]

We report a simple paper filter-based cross flow filtration method for air purification. We have examined a monolith filter array with a cross flow ratio of 1.0 and parallel and staggered filter arrays with a cross flow ratio of about 0.7 in terms of pressure drop and collection efficiency. The monolith filter array shows a monotonic increase in pressure drop from approximately 0.9 to 2.1 kPa. The parallel and staggered filter arrays reduce the increase in pressure drop, which can be maintained as low as 0.8 kPa over the entire range of dust loadings examined. The monolith filter array shows the highest collection efficiency, which is more than 95% over the entire range of dust loadings examined. The collection efficiency of the parallel and staggered filter arrays is initially as high as 70% and decreases to 30% when the dust loading increases to 40 and 100 g m−2, respectively. In particular, collected particles are more uniformly distributed on the staggered filter array than on the parallel filter array, resulting in the initial collection efficiency of 70% being sustained for a longer time. This uniform distribution in the staggered filter array may prevent a rapid increase in local pressure drop. This study provides insight into the development of filtration systems using simple paper filters without increasing the pressure drop and decreasing the collection efficiency. Copyright © 2022 American Association for Aerosol Research [ABSTRACT FROM AUTHOR]

Deterministic and statistical descriptions of parametric model uncertainties are discussed and illustrated with a case study from the paper industry. Prediction uncertainties under open loop and closed loop operation are then studied. The results illustrate the importance of a realistic description of parametric uncertainties, and also how closed loop operation can reduce the prediction sensitivity due to parameter uncertainties. [ABSTRACT FROM AUTHOR]

The determination of plotting positions on probability graph paper so that the associated weighted least squares estimators of the scale parameter and the percentiles of a continuous distribution have certain properties is discussed. Necessary and sufficient conditions are given for an invariant optimal plot for percentile estimation. Also discussed is the derivation of ordered plotting positions. [ABSTRACT FROM AUTHOR]

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

This paper addresses an unrelated parallel machines scheduling problem with the need of additional resources during the processing of the jobs, as well as during the setups that machines need between the processing of any two jobs. This problem is highly complex, and therefore in this paper we propose several constructive heuristics to solve it. To improve the performance of these heuristics, we propose several variations, including randomisation with different probability distributions and a local search phase, having this way GRASP algorithms. The results of extensive experiments over randomly generated instances show several findings on the different parameters that characterise our constructive algorithms. In particular, we highlight the fact that non-uniform probability distributions might be advisable for choosing elements of a restricted candidate list in GRASP algorithms. [ABSTRACT FROM AUTHOR]

Liseo and Loperfido [A note on reference priors for the scalar skew-normal distribution. J Statist Plann Inference. 2006;136(2):373–389] studied some peculiar features of default Bayes analysis of the scalar skew-normal model. In particular, they showed that, by considering the simplest model with a single unknown parameter λ of skewness, the reference – or Jeffreys’ – prior for this parameter is proper. They proved that tails of Jeffreys’ prior are of orderO(λ−3/2). But they made a mistake in their proof. In this note, we will modify their proof. [ABSTRACT FROM AUTHOR]

In the paper, we consider a three-dimensional mathematical problem of fluid-solid dynamical interaction, when an anisotropic elastic body occupying a bounded region Ω+ is immersed in an inviscid fluid occupying an unbounded domain Ω- = ℝ³ \ Ω++. In the solid region, we consider the generalized Green--Lindsay's model of the thermo-electro-magnetoelasticity theory. In this case, in the domain Ω+ we have a six-dimensional thermo-electro-magneto-elastic field (the displacement vector with three components, electric potential, magnetic potential, and temperature distribution function), while we have a scalar acoustic pressure field in the unbounded domain Ω-. The physical kinematic and dynamical relations are described mathematically by the appropriate initial and boundarytransmission conditions. Using the Laplace transform, the dynamical interaction problem is reduced to the corresponding boundary-transmission problem for elliptic pseudo-oscillation equations containing a complex parameter τ . We derive the appropriate norm estimates with respect to the complex parameter τ and construct the solution of the original dynamical problem by the inverse Laplace transform. As a result, we prove the uniqueness, existence, and regularity theorems for the dynamical interaction problem. Actually, the present investigation is a continuation of the paper [Chkadua G, Natroshvili D. Mathematical aspects of fluid-multiferroic solid interaction problems. Math Meth Appl Sci. 2021;44(12):9727--9745], where the fluid-solid interaction problems for elliptic pseudo-oscillation equations associated with the above mentioned generalized thermo-electromagneto- elasticity theory are studied by the potential method and the theory of pseudodifferential equations. [ABSTRACT FROM AUTHOR]

In this paper, we derive the asymptotic distributions of AugmentedDickey-Fuller (ADF) tests under very mild conditions. The tests were originally proposed and investigated by Said and Dickey (1984) for testing unit roots in finite-order ARMA models with i.i.d, innovations, and are based on a finite AR process of order increasing with the sample size. Our conditions are significantly weaker than theirs. In particular, we allow for general linear processes with martingale difference innovations, possibly having conditional heteroskedasticities. The linear processes driven by ARCH type innovations are thus permitted. The range for the permissible increasing rates for the AR approximation order is also much wider. For the usual t-type test, we only require that it increase at order o(n[sup ½]) while they assume that it is of order o(n[sub K]) for some k satisfying 0 < k ≤ 1/3. [ABSTRACT FROM AUTHOR]

This paper examines the random variation of the residual radius along the length of both naturally corroded and artificially corroded rebars. The rebars are washed to remove rust, and their residual area is measured by the water volume method for every 20-mm long segment of each rebar. Tests are carried out to determine the stationarity or non-stationarity of the stochastic field used to model the residual radius of the specimens. Then, the autocorrelation function, power spectrum and marginal probability distribution function of each specimen are estimated. It is found that the residual radius field of both naturally and artificially corroded rebars with mean corrosion levels below 20% is stationary, while the situation can change as the mean corrosion level increases and concrete cover spalling occurs. The residual radius field along the rebar length of stationary specimens is found to be white noise for both naturally and artificially corroded rebars. The marginal probability distribution function of the residual radius is determined to be skewed and can be fitted with a Beta distribution for naturally corroded rebars and with a Weibull distribution for artificially corroded rebars. This is the first paper studying and comparing both naturally and artificially corroded rebars. [ABSTRACT FROM AUTHOR]

In this paper, we propose Multi-View Dreaming, a novel reinforcement learning agent for integrated recognition and control from multi-view observations by extending Dreaming. Most current reinforcement learning method assumes a single-view observation space, and this imposes limitations on the observed data, such as lack of spatial information and occlusions. This makes obtaining ideal observational information from the environment difficult and is a bottleneck for real-world robotics applications. In this paper, we use contrastive learning to train a shared latent space between different viewpoints and show how the Products of Experts approach can be used to integrate and control the probability distributions of latent states for multiple viewpoints. We also propose Multi-View DreamingV2, a variant of Multi-View Dreaming that uses a categorical distribution to model the latent state instead of the Gaussian distribution. Experiments show that the proposed method outperforms simple extensions of existing methods in a realistic robot control task. [ABSTRACT FROM AUTHOR]

This paper investigates the potential of moment closures as a possible path to future quantum hydrodynamics models. Moment closures are known to produce accurate predictions of continuum and non-equilibrium classical gas flows while offering modeling and numerical advantages over other commonly used methods. The maximum-entropy hierarchy of moment closures holds the promise of robustly hyperbolic stable moment equations, however, the predicted distribution function in phase space is positive by design, which is in disagreement with the quasi-distribution function described by the Wigner equation. In this paper, predictions made by an interpolative one-dimensional five-moment system are compared to direct numerical solutions of the Wigner equation for a simple low-energy quantum state in unbounded doublewell potentials. Numerical solutions for a particle in various potentials described by quartic polynomials are presented. The capacity of moment methods to provide accurate and efficient models for quantum systems is explored. [ABSTRACT FROM AUTHOR]

The efficiency of material supply for workstations using Automatic Guided Vehicles (AGVs) is largely determined by the performance of the AGV dispatching scheme. This paper proposes a new solution approach for the AGV dispatching problem (AGVDP) for material replenishment in a general manufacturing workshop where workstations are in a matrix layout, and where uncertainty in replenishment time of workstations and stochastic unloading efficiencies of AGVs are dynamic contextual factors. We first extend the literature proposing a mixed integer optimisation model with a delivery satisfaction soft constraint of material orders and two objectives: transportation costs and delivery time deviation. We then develop a new knowledge-guided estimation of distribution algorithm with delivery satisfaction evaluation for solving the model. Our algorithm fuses three knowledge-guided strategies to enhance optimisation capabilities at its respective execution stages. Comprehensive numerical experiments with instances built from a real-world scenario validate the proposed model and algorithm. Results demonstrate that the new algorithm outperforms three popular multi-objective evolutionary algorithms, a discrete version of a recent multi-objective particle swarm optimisation, and a multi-objective estimation of distribution algorithm. Findings of this work provide major implications for workshop management and algorithm design. [ABSTRACT FROM AUTHOR]

This paper presents a new method for the feature screening of ultra-high dimensional data with response missing at random. The distribution function of the missing response is completed by imputation technology, and then the distance correlation between the imputed distribution function of response and the distribution function of covariate is used as an index for feature screening. The proposed method has the following advantages. First, it is a nonparametric model-free method, and can detect the nonlinear relationship between variables. Second, it is robust to covariates with outliers and heavy-tailed distributions. Third, it can deal with multi-dimensional response variables directly. Under certain assumptions, this paper demonstrates the sure screening and ranking consistency properties. Simulation studies are conducted to examine the performance of the proposed procedure and to compare with existing methods. Finally, our method is applied to the data analysis of diffuse large B-cell lymphoma. [ABSTRACT FROM AUTHOR]

The paper simulates systems in which two types of spin waves can occur, propagating in opposite directions. To achieve this, the quantum slow-wave approximation is employed, allowing for the determination of the probability distribution of occupied states in a quantum two-particle system subjected to perturbations, commonly referred to as Rabi oscillations. This model is specifically applied to a configuration of parallel nanowires exposed to an external electromagnetic wave within the microwave range. The study explores a potential application of the investigated nanostructures in the development of a device for detecting electromagnetic fields. [ABSTRACT FROM AUTHOR]

Kriging interpolation is a spatial interpolation method widely employed in the field of data analytics and prediction of environmental variables, which provides the best linear unbiased prediction of intermediate values. The core principle of Kriging interpolation is searching for data distribution regularity and predicting regionalised variable value, and it can be transferred into two descriptions of learning process: function fitting problem and coefficient optimisation problem. Although these two problems could be solved by many traditional algorithms like multiple linear regression method, the parameter estimation of variogram model becomes quite difficult when there are drifts or noises in the raw data. The purpose of this paper is to improve the Kriging interpolation algorithm with learning kernels based on Estimation of Distribution Algorithms (EDAs) and Least-Squares Support Vector Machine (LSSVM). The experiments have been carried out based on a real-world case with environmental variables. Compared with other machine learning methods, experimental results verify the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This paper aims to propose a Novel Condition-based maintenance (CBM) decision aid model for optimising the maintenance of complex multi-component systems. As the degradation level of each component is assumed to be independent and stochastic, it follows a specific probability distribution determined from historical data of experimental observations and inspection. The main objective is to optimise the total cost for providing maintenance actions and reducing the excess of spare parts usage. The decision support model consists of determining measurements on components with the aim of estimating the instant of time of removing predictively one or a group of components before they fail. The measurement model includes the mean residual lifetime (MRL) and some extensions developed for this purpose. For demonstrating the pertinency of the proposed model, we use a preventive maintenance strategy for one-component systems and a grouping/opportunistic maintenance for multi-component systems. Besides, a numerical comparative study performing these measurements is carried out using several examples and a case study from Electric energy distribution systems. The solution is illustrated as a decision-making optimal model for optimising the maintenance operations' costs and the total number of spare parts. The numerical results and the comparison show the efficiency of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper presents interval estimation for the population mean and coefficient of variation in a two-parameter exponential distribution. The new generalized pivot, profile likelihood function and likelihood ratio statistic are derived and used to construct the confidence intervals. A highlight of this paper is that the generalized and likelihood ratio confidence intervals for the mean and coefficient of variation perform well in terms of coverage probability in many cases. Finally, two real-data applications on the air pollution of particulate matter (PM2.5) and the renewable energy through wind power of Thailand are used for illustration purposes. [ABSTRACT FROM AUTHOR]

Conceptual pre-estimation of road tunnel costs is a vital yet challenging process during feasibility studies due to the prevailing underground uncertainties and risks. Most existing cost estimation approaches are deterministic, probabilistic methods are limited to a single cost examination. This paper introduces a probabilistic model for pre-estimating road tunnels life-cycle costs. It aims to capture their inherent uncertainty holistically, thus enabling more reliable decision-making at a project's early stages. The proposed model is developed in three steps: multiple regression analysis, fitting distribution, and Monte-Carlo simulation. The first step unveils the correlations between independent and dependent variables, while the other two steps return the probabilistic descriptions of cost drivers and life-cycle costs. Civil engineering, electromechanical works costs, energy consumption, and operation & maintenance costs are determined as the model's output variables. A real-world database of 32 dual-bore road tunnels with a total length of 55 km is used to develop probability distributions within reasonable confidence intervals and a sensitivity analysis was performed utilizing tornado charts. The results can assist public authorities and managers in estimating the probability of a specific life-cycle cost and making appropriate decisions in accordance with their risk tolerance. [ABSTRACT FROM AUTHOR]

In many real-world situations, systems frequently fail in their demanding operational settings. Researchers pay little attention to the fact that systems typically fail to execute their intended activities when it reaches its extreme operating situations as appropriate. In this paper, we try to develop and study inferential aspect of a system reliability having multiple components based on a progressive first failure censoring scheme assuming unit length-bias exponential distribution. Regarding estimation, asymptotic, boot-p, and boot-t approaches under the interval estimation are adopted, while the maximum likelihood method under the point estimation is considered. The MCMC method is used to get the Bayes estimate of the reliability parameter assuming both the symmetric and asymmetric loss functions. The associated confidence intervals are also reported as appropriate. The effectiveness of the various adopted estimation strategies is evaluated and compared using Monte Carlo simulation studies and examples from real-world applications. [ABSTRACT FROM AUTHOR]

This paper presents a novel probabilistic data-driven approach to trip-level energy consumption estimation of battery electric vehicles (BEVs). As there are very few electric vehicle (EV) charging stations, EV trip energy consumption estimation can make EV routing and charging planning easier for drivers. In this research article, we propose a new driver behavior-centric EV energy consumption estimation model using probabilistic neural networks with model uncertainty. By incorporating model uncertainty into neural networks, we have created an ensemble of neural networks using Monte Carlo approximation. Our method comprehensively considers various vehicle dynamics, driver behavior, and environmental factors to estimate EV energy consumption for a given trip. We propose relative positive acceleration (RPA), average acceleration, and average deceleration as driver behavior factors in EV energy consumption estimation, and this paper shows that the use of these driver behavior features improves the accuracy of the EV energy consumption model significantly. Instead of predicting a single-point estimate for EV trip energy consumption, this proposed method predicts a probability distribution for the EV trip energy consumption. The experimental results of our approach show that our proposed probabilistic neural network with weight uncertainty achieves a mean absolute percentage error of 9.3% and outperforms other existing EV energy consumption models in terms of accuracy. [ABSTRACT FROM AUTHOR]

In this paper, studies of competing risks model are considered when the observations are left-truncated and right-censored data. When the failure times of the competing risks are distributed by a generalized inverted exponential model with same scale but different shape parameters with partially observed failure causes, statistical inference for the unknown model parameters is discussed from classical and Bayesian approaches, respectively. Maximum likelihood estimators of the unknown parameters, along with associated existence and uniqueness, are established, and the asymptotic likelihood theory is also used to construct the confidence interval via the observed Fisher information matrix. Moreover, Bayesian estimates and the corresponding highest posterior density credible intervals are also obtained based a flexible Gamma-Beta prior, and a Gibbs sampling technique is constructed to compute associated estimates. Further, under a general practical assumption with order-restriction parameter case, classical and Bayesian estimations are also established under order restriction situations, respectively. Extensive Monte-Carlo simulations are carried out to investigate the performances of our results and two real-life examples are analyzed to show the applicability of the proposed methods. [ABSTRACT FROM AUTHOR]

This paper makes a game-theoretic analysis of an M/M/1 queue with variable vacation and vacation interruptions. The Nash equilibrium mixed strategy and social utility maximization are derived based on a non-cooperative game theory and an optimization theory under different information precision levels, namely almost unobservable and fully unobservable cases. The explicit solutions of the entrance probabilities and the steady-state probability distribution of the system are investigated using the probability generating function and nonhomogeneous linear difference equations. Furthermore, the effects of the information levels and diverse system parameters on the equilibrium strategies, the arrival rates, and the expected benefits are explicitly illustrated by numerical comparisons. The research results can provide a theoretical basis and performance analysis tool for the optimal design in the wireless transmission and network communication system. [ABSTRACT FROM AUTHOR]

An extension of the omnibus test statistic of Ebner et al. [A new omnibus test of fit based on a characterization of the uniform distribution. Statistics. 2022;56:1364–1384. doi: 10.1080/02331888.2022.2133121] is considered for the general two-sample alternative. In addition, using the extension this paper introduces a maximum test statistic and an adaptive test statistic for testing the equality of two distributions. The power performance in various situations is investigated for continuous and discrete distributions. Simulation studies based on Monte-Carlo show that the proposed test statistics are good competitors of the existing nonparametric test statistics. The proposed test statistic displays outstanding performance in certain situations, and is illustrated using real data. Finally, we offer some concluding remarks. [ABSTRACT FROM AUTHOR]

Designing a green supply chain is becoming popular in the context of sustainable development. To address this academic concern, this paper designs a multi-product, multi-echelon green supply chain network (GSCN) from economic and environmental aspects. During the modeling process, the main challenge is to access the accurate probability distributions of uncertain parameters from limited historical data. To overcome this difficulty, this paper develops a distributionally robust design framework for bi-objective GSCN, where the distribution information of uncertain parameter is partially available and characterized by ambiguity sets. For the tractability, this paper discusses robust counterpart reformulation under Wasserstein-distance-based ambiguity sets. Finally, the obtained mixed integer programming model is resolved via commercial optimization software. To validate the proposed optimization framework, we design a meat supply chain network for a Chinese realistic food enterprise. The computational results demonstrate that the proposed distributionally robust model can provide reliable solutions compared with stochastic optimization method. [ABSTRACT FROM AUTHOR]

This paper presents a novel moving horizon estimation approach based on distributionally robust optimisation to tackle the state estimation problem of non-linear systems with missing noise distribution information. The proposed method adopts a fuzzy set to mitigate the impact of uncertainties on state estimation. Specifically, the method derives an empirical distribution within the prediction window using a priori data and constructs a fuzzy sphere set using the Wasserstein metric with the empirical distribution as the sphere centre. This enables the estimation of the state sequence under the worst probability distribution of the fuzzy set. To demonstrate the effectiveness of the proposed method, a simple simulation example is conducted to compare its performance with that of traditional moving horizon estimation. The results provide evidence of the feasibility and superiority of the proposed approach. [ABSTRACT FROM AUTHOR]

Planning decisions are generally subject to some level of uncertainty. In forestry, data describing the resources available have a major impact on operations performance and productivity. This paper aims to present a method to improve decision-making in the forest supply chain by taking supply uncertainty into account using the results of data quality assessments. The case study describes the operations planning process of a Canadian forest products company dealing with an uncertain volume of wood supply. Three approaches to constructing probability distributions based on data quality are tested. Each approach offers a different level of precision: (1) a frequency distribution of accuracy, (2) a normal distribution based on average accuracy, and (3) a normal distribution based on data quality classification. Using stochastic programming to plan transport and production shows that lower costs can be achieved with a general characterisation of the data accuracy. Not considering uncertainty when planning operations leads to a significant replanning transportation cost. Using classes of data quality to include uncertainty in operations planning contributes to reducing the transportation cost from $15.90/m3 down to $15.32/m3 representing 3.6%. [ABSTRACT FROM AUTHOR]

In this work, we investigate spacings based on order statistics obtained from continuous distribution functions. At the beginning of the paper, we present distributional results for spacings and a method of classification of distributions according to their tails. Then we use this method to derive asymptotic results for spacings. By applying some special versions of Borel–Cantelli lemma, we obtain their strong limit results. At the end of the paper, we present some illustrative examples. [ABSTRACT FROM AUTHOR]

Let F be a continuous distribution function and let Q be its associated quantile function. Let Fh be the kernel estimator of F and Qh that of Q. In this article the L2 right inversion distance between Qh and Q is introduced. It is shown that this distance can be represented in terms of Fh and F, more precisely it is established that the right inversion distance is equal to the conventional integrated squared error between Fh and F. This representation shows that any good bandwidth for Fh is a reasonable bandwidth for Qh and, this fact enables us to suggest methods to choose the smoothing parameter of Q h. Let Q h ̂ c v be the kernel estimator of Q equipped with the global crossvalidation bandwidth h ̂ c v designed for F h. Let Q h ̂ p i be the linear kernel estimator of Q, h ̂ p i being the plug-in bandwidth function. A small scale simulation study presented in this paper contains some examples of distributions for which Q h ̂ c v appears to be superior to Q h ̂ p i . This paper also contains some properties of the classical L2 distance between Qh and Q. [ABSTRACT FROM AUTHOR]

To avoid either idle servers or an over-congested situation, we analyse a queueing system with a variable number of servers. Specifically, if the queue length exceeds an upper threshold, all of the servers are serving customers, and if the number of idle servers reaches a threshold (or the number of customers is below a lower threshold), these idle servers are turned off. We call this policy Congestion-Based Staffing (CBS) with two thresholds. Optimising these thresholds under a certain cost structure is the focus of this paper. The key factor in modelling a manufacturing or service system with random service requests by a queueing model is to realistically model the random service times. Although the exponential distribution has been used successfully to model the service times of a call centre, it is not appropriate for manufacturing or service systems. We propose to use a Phase-type (PH) distribution for modelling the service times in a manufacturing system, as it is more flexible and can fit any shape of distribution in theory. Therefore, we build an M/PH/C model with the CBS policy and develop a solution procedure for computing the queue length stationary distribution. Based on this stationary distribution, we investigate a real-world system in the Shanghai Baoshan Iron and Steel Complex. Using the real data and a realistic cost structure, we determine the optimal CBS policy in terms of minimising the operating cost. This policy yields an operating cost that is considerably smaller than the operating cost under a practical policy. [ABSTRACT FROM AUTHOR]

Although automated storage/retrieval systems (AS/RSs) with two depots at opposite ends of each aisle (TD-AS/RSs) have been adopted in I-shaped warehouses (one of the three typical warehouse layouts), class-based storage policy has surprisingly not been investigated in TD-AS/RSs. This paper studies TD-AS/RSs with two storage zones, aiming to determine the optimal first storage zone that minimises the S/R machine's expected travel time. We first formulate an expected travel time model. The analysis is then performed for two situations: (1) the ratio between the number of storage and total requests (Ratio-ST) is constant and (2) the Ratio-ST changes with time but follows a probability distribution. For the first situation, utilising proposed properties, an efficient optimal search-based algorithm (i.e. Algorithm 1) is developed. The results show that the proposed storage policy can improve system performance by up to about 60% and 40%, respectively, compared with two policies used in practice. Contrary to the literature results, our results indicate that the single command cycle performs better than the dual command cycle in the TD-AS/RS. For the second situation, an algorithm based on Algorithm 1 is developed. A case study using two real-world datasets confirms that our policy outperforms practically used policies in this situation. [ABSTRACT FROM AUTHOR]

The Beale Papers is an 1885 pamphlet in which there are three ciphers, said to contain the location of a hidden treasure. In this paper the ciphers are viewed through Benford's Law. Statistical analysis show that the the ciphers deviate from the law—cipher 2 less so than 1 & 3. Furthermore the numbers in the uncracked ciphers do not come from the same distribution as the cracked one, but it seems that the uncracked ciphers might share a similar random distribution. One possible explanation is that cipher 1 & 3 are faked in a similar manner, another is that they might share the same key. [ABSTRACT FROM AUTHOR]

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

This paper presents the impact of adding single-phase photovoltaic systems on the fault current of short-circuit faults in asymmetric 400 V low-voltage feeders. This study also attempts to investigate the impact of various parameters on the fault current, such as the penetration coefficient of photovoltaic systems, the impact of downstream or upstream fault on the system installation location, and distance of photovoltaic systems and fault location. Simulations were carried out in the DIgSILENT software. The results show that the fault current will be more different when using photovoltaic systems and that difference is sometimes incremental and sometimes decremental. Therefore, if the penetration coefficient of the system is high, it will sometimes have a significant impact on the protection system. [ABSTRACT FROM AUTHOR]

Two-parameter exponential distributions have a widespread application in insurance, medical and industrial production. However, incomplete samples are often obtained due to experimental conditions. In this paper, a new adaptive exponentially weighted moving average control chart, called AEWMA-LR control chart, is proposed for monitoring the quality characteristics of two-parameter exponential distributions based on type-II censored data. The proposed monitoring scheme aims to achieve an adaptive effect by combining exponentially weighted moving averages and adjusting the weight factors according to the relative magnitude of the estimated location and scale parameter shifts. We explored the effects of smooth parameters, sample size, and censored parameters on the performance of AEWMA-LR control charts through a Monte Carlo simulation study. Then, a comparative analysis was conducted with existing EWMA-LR and EWMA-Max-MLE control charts based on the two-parameter exponential model. The simulation results of zero-state average run length (ARL) and conditional expected delay (CED) show that the proposed monitoring scheme outperforms the existing control charts. Finally, to demonstrate the usefulness of the AEWMA-LR control chart in real-world applications, we give three instances of two-parameter exponential distributions based on type-II right censored data. [ABSTRACT FROM AUTHOR]

The shared frailty models are now popular for modelling heterogeneity in survival analysis. It assumes that the same frailty is shared by all individual members within the families. Also, it is believed that all the individuals in the population are susceptible to the event of interest and will eventually experience the event. This may not always be the situation in reality. There may be a certain fraction of the population which is non-susceptible for an event and hence may not experience the event under study. Non-susceptibility is modelled by frailty models with compound frailty distribution. Further, susceptibility may be different for different families. This can be attained by randomizing the parameter of frailty distribution. This paper incorporates both the things, non-susceptibility and different susceptibility for different families by considering compound negative binomial distribution with random probability of susceptibility as frailty distribution. The inferential problem is solved in a Bayesian framework using Markov Chain Monte Carlo methods. The proposed model is then applied to a real-life data set. [ABSTRACT FROM AUTHOR]

This paper proposes to utilise an innovative transformation KDE (Kernel Density Estimation) method in order to more accurately calculate the sea state parameter distribution tails and to extrapolate well. This transformation KDE method is applied in predicting the probability distribution tails of a measured ocean wave dataset at National Data Buoy Center Station 51101, and its accuracy has been verified through comparisons with the prediction results via the parametric method. Next, the transformation KDE method is utilised for deriving an accurate 50-year environmental contour line based on the aforementioned measured wave dataset. The derived environmental contour line and some other contour lines obtained using parametric contour approaches are then applied for predicting the 50-year design PTO (Power-Take-Off) force values for a point absorber Wave Energy Converter (WEC). It is concluded that the predicted 50-year design PTO force value based on the proposed transformation KDE contour is more accurate. [ABSTRACT FROM AUTHOR]

Presents a response to a letter to the editor of the 'Communications in Statistics--Theory and Methods,' concerning the study 'A multivariate generalization of the power exponential family of distributions.' Reference to other studies on the symmetric Kotz type distribution; Characteristics functions of the power exponential distribution.

We consider two classes of exponential dispersion models of discrete probability distributions which are defined by specifying their variance functions in their mean value parameterization. These classes were considered in our earlier paper as models of overdispersed zero-inflated distributions. In this paper we analyze the application of these classes to fit count data having overdispersed and zero-inflated statistics. For this reason, we first elaborate on the computational aspects of the probability distributions, before we consider the data fitting with our models. We execute an extensive comparison with other statistical models that are recently proposed, on both real data sets, and simulated data sets. Our findings are that our framework is a flexible tool that gives excellent results in a wide range of cases. Moreover, specifically when the data characteristics show also large skewness and kurtosis our models perform best. [ABSTRACT FROM AUTHOR]

This paper proposes a new design method for a stochastic control policy using a normalizing flow (NF). In reinforcement learning (RL), the policy is usually modeled as a distribution model with trainable parameters. When this parameterization has less expressiveness, it would fail to acquiring the optimal policy. A mixture model has capability of a universal approximation, but it with too much redundancy increases the computational cost, which can become a bottleneck when considering the use of real-time robot control. As another approach, NF, which is with additional parameters for invertible transformation from a simple stochastic model as a base, is expected to exert high expressiveness and lower computational cost. However, NF cannot compute its mean analytically due to complexity of the invertible transformation, and it lacks reliability because it retains stochastic behaviors after deployment for robot controller. This paper therefore designs a restricted NF (RNF) that achieves an analytic mean by appropriately restricting the invertible transformation. In addition, the expressiveness impaired by this restriction is regained using bimodal student-t distribution as its base, so-called Bit-RNF. In RL benchmarks, Bit-RNF policy outperformed the previous models. Finally, a real robot experiment demonstrated the applicability of Bit-RNF policy to real world. [ABSTRACT FROM AUTHOR]

Experience in the UK with auto enrolling workers in pensions indicates that once enrolled, most workers stay enrolled, suggesting that auto enrollment may be a desirable policy for other countries. However, the experience with auto enrollment is much different in Poland. This paper examines the argument that inertia is not a strong force when workers distrust in the security of future pension benefits. We present a simple conceptual framework where trust affects the subjective probability distribution of workers relating to future pension benefits. We investigate how this framework might explain the high opt-out rate in Poland. [ABSTRACT FROM AUTHOR]

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

A shortcoming of the typical use of the frequentist probabilistic approach in reliability analysis of limit state equations that appear in the geotechnical literature is that estimates of the uncertainty in reliability index (probability of failure) are not made. A Bayesian approach is demonstrated in the paper to overcome this shortcoming using the example of the pullout limit state for internal stability of mechanically stabilised earth (MSE) walls. The paper shows that in the Bayesian context, reliability index or probability of failure are modelled as probability distributions, and therefore readily incorporate the uncertainty in their estimates. The general approach provides a tool to communicate the level of risk to stakeholders that follows from the choice of design method and guidance to reduce uncertainty on the estimate of reliability. For practical purposes, the predictive reliability index may be used as an alternative measure of margin of safety that takes this uncertainty into account. [ABSTRACT FROM AUTHOR]

Natural Gas Hydrate (NGH) downhole hydrocyclone separator is one of the core components of solid-state fluidized mining method, and its adaptability to NGH reservoir parameters directly determines the success of future commercial NGH mining. In this paper, CFD method is used to study the performance of downhole small-size hydrocyclone separator with classical structure under the condition of NGH solid-state fluidization. In this paper, NGH recovery efficiency, sand removal efficiency and pressure drop are taken as evaluation indexes, and the influences of sand size, inlet sand and NGH volume fraction are studied. The simulation successfully obtained the distribution of each discrete phase in the separator. The separation efficiency and pressure drop of the separator are calculated. It is found that when the inlet sand particle size is too low, both sand removal and NGH recovery efficiency are very poor. As the inlet sand volume fraction increases, the hydrate column gradually disappears and the sand aggregation area eventually exceeds the locus of zero vertical velocity. And as the inlet NGH volume fraction increases, the lip leakage effect increases. This study provides the basis for the use of downhole separators in solid-state fluidized mining process and the design and optimization of related separators. [ABSTRACT FROM AUTHOR]

The spatial and spatio-temporal dependence modeling to extreme value distributions have been used to analyze the extremes of daily maximum rainfall data across selected weather stations in South Africa combining generalized Pareto distribution (GPD) with the flexible Bayesian Latent Gaussian Model (LGM). The paper demonstrated the spatio-temporal GPD model for applications in extreme rainfall data that capture systematic variation through spatial and spatio-temporal modeling framework, in which the temporal constitutes the week and month as random separately. The paper uses the Bayesian integrated Nested Laplace approximation (INLA) algorithm to estimate marginal posterior means of the parameters and hyper-parameters for Bayesian spatio-temporal models. The Bayesian inferences using INLA technique were applied to obtain prediction of the return levels at each station, which incorporate uncertainty due to model estimation, as well as the randomness that is inherent in the processes. [ABSTRACT FROM AUTHOR]

Various objective priors have been defined for the common correlation coefficient concerning several bivariate normal populations. In this paper, the proposed approach relies on the asymptotic matching of coverage probabilities corresponding to Bayesian credible intervals considering the corresponding frequentist ones. In the present paper, we focus on several matching criteria including quantile matching, distribution function matching, highest posterior density matching, and matching via inversion of test statistics. In addition, we consider reference priors for different groups of ordering. The proposed methods are investigated and compared between each other in terms of a frequentist coverage probability and then, they are illustrated through a simulation study and two real data examples. [ABSTRACT FROM AUTHOR]

Many tour providers have pinned their hopes on providing virtual tours to bring back visitors in the ongoing coronavirus disease 2019 (COVID-19) pandemic. In this paper, we develop an analytical model to examine whether free virtual tours can help attract more visitors. We consider a tour provider deciding whether to provide a free virtual tour and its grade if any is provided to maximize visitors' physical presence. Potential visitors possess heterogeneous preferences and perceived equivalence, and the tour provider knows only their respective random distributions. The model is solved to maximize tour providers' physical demand. Our analysis finds that a free virtual tour can help if potential visitors significantly underestimate the physical tour and identifies the critical threshold; we also find that the COVID-19 pandemic reduces the likelihood that a free virtual tour can help. This paper contributes to the tourism management community by accentuating the dark side of virtual tours, suggesting that tour providers should be prudent before introducing any virtual tour. We also provide guidelines for virtual tourism, helping tour providers respond to and recover from the COVID-19 pandemic and other uncertain situations. [ABSTRACT FROM AUTHOR]

The beta generator technique entails constructing a univariate distribution function as a composite function of two distribution functions. The success of this technique in the univariate setting has prompted research into the possibility of generalization to the bivariate case. Such a generalization, using copulas, has already been proposed in the literature. In this paper, we construct bivariate distribution functions by passing a bivariate distribution function as an argument to the univariate beta distribution function. The class of distributions obtained is identical to an existing class of distributions; however, the elementary elements of the two classes differ (i.e., some distributions are simple to construct using one of the techniques considered and difficult to construct using the other). This paper provides a rigorous derivation of the parameter space of the beta-generated distributions, as well as a result relating to the dependence structure of the marginals. Finally, a practical example is included demonstrating the use of a beta-generated distribution in the modeling of observed losses in the energy market. [ABSTRACT FROM AUTHOR]

In this paper, research results are presented and discussed on the efficient use of additive manufacturing (AM) machine workspace with a specific focus on the features of part construction and decomposition, which provide savings of material and energy. Statistical analysis of the distribution of material by subspaces revealed some relationship between construction features and the effectiveness of part decomposition. The initial triangulated model was converted into a voxel model, and the latter is analyzed with the proposed algorithm. The workspace of an AM machine was divided into subspaces of the same volume with parallel steadily distributed planes perpendicular to the coordinate axes. Based on the models of typical industrial parts, it was proving that the algorithm was able to analyze the effectiveness of part decomposition. Moreover, some indexes were proposed to allow the quantitative analysis of part decomposition and packing (workspace planning task) effectiveness. The proposed index of the specific volume of utilised workspace enabled the minimising of the cost of given parts by using AM processes. [ABSTRACT FROM AUTHOR]

This paper investigates the power performance of five tests, including improved versions of two existing tests, for jointly testing the equality of origin and scale parameters of two samples from a shifted (two-parameter) exponential distribution. The power of the test varies with a shift in either or both of the two parameters. Therefore, a power surface is observed for various tests. Different tests are optimal for different shift sizes. This paper also compares the volume under the five tests' power surfaces to determine an overall best when the shift size is unknown. The generalized likelihood ratio (GLR) test, the Bayoud and Kittaneh test based on Weitzman's overlapping coefficient, recently designed Max and Distance tests, and an improved likelihood-based procedure are compared. The shifted exponential distribution is often an appropriate probability model for the lifetime of a product with a warranty, high voltage current in specific semiconductor transistors, and military personnel vehicles' mileages that failed in operation. The number of survival days for patients with irreversible lung cancer often follows the same distribution. This distribution plays a vital role in the engineering and biomedical sciences. We observe that the newly designed tests and the exact GLR test are almost always preferable to the other tests. We illustrate the proposed exact test procedures with two practical examples. [ABSTRACT FROM AUTHOR]