Extremes of multivariate ARMAX processes

We define a new multivariate time series model by generalizing the ARMAX process in a multivariate way. We give conditions on stationarity and analyze local dependence and domains of attraction. As a consequence of the obtained results, we derive new multivariate extreme value distributions. We characterize the extremal dependence by computing the multivariate extremal index and bivariate upper tail dependence coefficients. An estimation procedure for the multivariate extremal index is presented. We also address the marginal estimation and propose a new estimator for the ARMAX autoregressive parameter.     

On extremal dependence: some contributions

The usual coefficients of tail dependence are based on exceedances of high values. These extremal events are useful and widely used in literature but an adverse situation may also occur with the upcrossing of a high level. In this context we define upcrossings-tail dependence coefficients and analyze all types of dependence coming out. We will prove that these coefficients are related to multivariate tail dependence coefficients already known in literature. We shall see that the upcrossings-tail dependence coefficients have the interesting feature of congregating both ??temporal?? and ??spatial?? dependence. The coefficients of tail dependence can also be applied to stationary sequences and hence measure the tail dependence in time. Results concerning connections with the extremal index and the upcrossings index as well as with local dependence conditions will be stated. Several illustrative examples will be exploited and a small note on inference will be given by presenting estimators derived from the stated results and respective properties.     

Rising tail in Bradford distribution: Its interpretation and application

The right tail of the Bradford distribution has been considered to be straight or drooping. This paper reports cases in which the right tail is rising upward, explains and verifies conditions of its occurrences, interpretes it and proposes its application to evaluation and forecasting of technological development at the basic research stage.     

Improving extremal fit: a Bayesian regularization procedure

In structural reliability, special attention is devoted to model distribution tails. The distributions are required to fit the upper observations and provide a picture of the tail above the maximal observation. Goodness-of-fit tests can be constructed to check this tail fit. Then what can we do with distributions having a good central fit and a bad extremal fit? We propose a regularization procedure. It is based on Bayesian tools and takes into account the opinion of experts. Predictive distributions are proposed as model distributions. We numerically investigate this method on normal, lognormal, exponential, gamma and Weibull distributions.     

Four-parameter Weibull probability distribution model for weakly non-linear random variables

The use of multi-parameter distribution functions that incorporate empirically derived parameters to more accurately capture the nature of data being studied is investigated. Improving the accuracy of these models is especially important for predicting the extreme values of the non-linear random variables. This study was motivated by problems commonly encountered in the design of offshore systems where the accurate modeling of the distribution tail is of significant importance. A four-parameter Weibull probability distribution model whose structural form is developed using a quadratic transformation of linear random variables is presented. The parameters of the distribution model are derived using the method of linear moments. For comparison, the model parameters are also derived using the more conventional method of moments. To illustrate the behavior of these models, laboratory data measuring the time series of wave run-up on a vertical column of a TLP structure and wave crests interacting in close proximity with an offshore platform are utilized. Comparisons of the extremal predictions using the four-parameter Weibull model and the three-parameter Rayleigh model verify the ability of the new formulation to better capture the tail of the sample distributions.     

The ‘Industrial Enlightenment’ and technological paradigms of the modern steel industry

Scientific knowledge is crucial to opening up new possibilities for major technological advances. When did science become important for economic development? The steam engine was the earliest major science-based invention. Conversely, the role of science has not been regarded as important in the innovations leading to modern steelmaking. In addition, how did science begin to play an important role? Mokyr focuses on the ‘Industrial Enlightenment’, which has its origins in the Baconian program of the seventeenth century. However, the role of science is often not regarded as important in the emergence of modern steelmaking technology. This paper examines the process through which modern steelmaking emerged and clarifies the role of science and ‘Industrial Enlightenment’. This discussion is also important in determining how to view the role of science in economic development and in considering ‘the Great Divergence’ and ‘the Great Knowledge Transcendence’. In addition, the examination of this paper will show how to create radical innovations that are completely different from existing paradigms, and how to create new technological paradigms to overcome difficulties such as the recent Covid-19 pandemic and environmental problems. When much time elapses between scientific and technological advances, the role of science is often not regarded as important and sensational innovations such as the Bessemer process are emphasized. However, this is not a proper evaluation. The role of ‘Industrial Enlightenment’ on the supply side must also be recognized as significant in the emergence of modern steelmaking technology.     

The multivariate extremal index and the dependence structure of a multivariate extreme value distribution

LetH be the limiting distribution of a vector of maxima for ad-dimensional stationary sequnce with multivariate extremal index. We giv necessary and sufficient conditions forH to have independent or totally dependent margins by using relations between the multivariate extremal index and the univariate extremal indexes. A new functional family of multivariates extreme value distributions, containingH, is introduced. We apply the results to characterize the asymptotic independence of the maximum and the minimum and compute the multivariate extremal index of the Multivariate Maxima of Moving Maxima process.     

Extreme and first excursion probability

Abstract

The extreme value problem is related to the first excursion problem in random vibration analysis. In the present paper, Gumbel's order statistics and the asymptotic theory of statistical extremes are applied directly to the peak distribution function of a stationary random process in order to find the probability distribution of the extremal value within a certain time interval. The extreme value distribution of a random process obtained from this approach is compared with results from some classical methods. It is concluded that the present approach can be applied not only to a narrow‐band process but also to a wide‐band process for which the classical methods usually use several approximations to find the approximate results. The second part of this paper deals with the first excursion probability. A semi‐empirical formula based on results of the first part and a correlation time consideration are proposed. Three examples, which include a narrow‐band process, a wide‐band process and a uniformly modulated process, are studied. The results are compared favorably with either simulation results or those obtained from other methods.     

热轧带钢尾部横裂缺陷的成因及解决

热轧过程中对于厚规格产品，易发生尾部横裂缺陷，经分析其产生原因是由于粗轧过程中板带尾部局部温降大，从而在变形过程中由于延伸不均而造成横向裂纹，通过改善板型及冷却条件，可以很好的解决这一问题。     

Extremal properties of M4 processes

The existence of data with different dependence structures motivates the development of models which can capture several types of dependence. In this paper we consider a stationary sequence of moving maxima vectors \(\{{\mathbf {X}}_n=(X_{n1},\ldots ,X_{nd})\}_{n\ge 1}\) having innovations \({\mathbf {Z}}_{l,n}=(Z_{l,n,1},\ldots ,Z_{l,n,d})\) with totally dependent margins for certain values of \(l,\) \(l\in I_1,\) and independent margins for the remaining values of \(l,\) \(l\in I_2.\) We obtain in this way a \(d\) -dimensional process \(\{{\mathbf {X}}_n\}_{n\ge 1}\) whose extremal dependence, measured by the tail dependence coefficients, lies between asymptotic independence and total dependence. The extremal properties of these M4 processes are studied and examined both theoretically and through simulation studies: we derive the multivariate extremal index, the tail dependence coefficients and co-movement indices.     

The law of limited excellence: publication productivity of Israel Prize laureates in the life and exact sciences

The present paper extends Lotka’s theorem—which we rename as “the law of limited excellence”—while empirically modelling the scientific productivity of 46 Israel Prize laureates in the life and exact sciences—a group best described as ‘Star Scientists’. By focusing on this highly selective group we expose unequal scientific productivity even amongst Israel’s most prolific scientists. Specifically, we test the invariance of Lotka’s law by focusing attention on the extreme tail of publication distributions while empirically exploring the non-linearity of its seemingly “flat” tail. By exposing the rarity of excellence even in this extreme end of publication productivity we extend the generality of Lotka’s theorem and expose that—like a fractal—the tail of excellence behaves as the entire distribution. We end this empirical contribution by suggesting a few implications for research and policy.     

Model Misspecification of Generalized Gamma Distribution for Accelerated Lifetime-Censored Data

Abstract

The performance of reliability inference strongly depends on the modeling of the product’s lifetime distribution. Many products have complex lifetime distributions whose optimal settings are not easily found. Practitioners prefer to use simpler lifetime distribution to facilitate the data modeling process while knowing the true distribution. Therefore, the effects of model mis-specification on the product’s lifetime prediction is an interesting research area. This article presents some results on the behavior of the relative bias (RB) and relative variability (RV) of pth quantile of the accelerated lifetime (ALT) experiment when the generalized Gamma (GG₃) distribution is incorrectly specified as Lognormal or Weibull distribution. Both complete and censored ALT models are analyzed. At first, the analytical expressions for the expected log-likelihood function of the misspecified model with respect to the true model is derived. Consequently, the best parameter for the incorrect model is obtained directly via a numerical optimization to achieve a higher accuracy model than the wrong one for the end-goal task. The results demonstrate that the tail quantiles are significantly overestimated (underestimated) when data are wrongly fitted by Lognormal (Weibull) distribution. Moreover, the variability of the tail quantiles is significantly enlarged when the model is incorrectly specified as Lognormal or Weibull distribution. Precisely, the effect on the tail quantiles is more significant when the sample size and censoring ratio are not large enough. Supplementary materials for this article are available online.     

Bias-corrected and robust estimation of the bivariate stable tail dependence function

The stable tail dependence function gives a full characterisation of the extremal dependence between two or more random variables. In this paper, we propose an estimator for this function which is robust against outliers in the sample. The estimator is derived from a bivariate second-order tail model together with a proper transformation of the bivariate observations, and its asymptotic properties are studied under some suitable regularity conditions. Our estimation procedure depends on two parameters: \(\alpha \), which controls the trade-off between efficiency and robustness of the estimator, and a second-order parameter \(\tau \), which can be replaced by a fixed value or by an estimate. In case where \(\tau \) has been replaced by the true value or by an external consistent estimator, our robust estimator is asymptotically unbiased, whereas in case where \(\tau \) is mis-specified, one loses this property, but still our estimator performs quite well with respect to bias. The finite sample performance of our robust and bias-corrected estimator of the stable tail dependence function is examined on a simulation study involving uncontaminated and contaminated samples. In particular, its behavior is illustrated for different values of the pair \((\alpha , \tau )\) and is compared with alternative estimators from the extreme value literature.     

Local robust and asymptotically unbiased estimation of conditional Pareto-type tails

We introduce a non-parametric robust and asymptotically unbiased estimator for the tail index of a conditional Pareto-type response distribution in presence of random covariates. The estimator is obtained from local fits of the extended Pareto distribution to the relative excesses over a high threshold using an adjusted minimum density power divergence estimation technique. We derive the asymptotic properties of the proposed estimator under some mild regularity conditions, and also investigate its finite sample performance with a small simulation experiment. The practical applicability of the methodology is illustrated on a dataset of calcium content measurements of soil samples.     

化工尾气中氢气和乙烯的低温精馏回收工艺流程的设计与优化分析

化工尾气对环境污染严重,但是其中含有的氢气和乙烯具有较高的回收利用价值。针对某一化工尾气,采用低温液化精馏工艺对其中的氢气和乙烯进行分离。运用HYSYS软件进行化工尾气中氢气和乙烯低温精馏工艺流程的模拟与优化分析,给出了工艺流程中关键点的技术参数。分析结果显示,氢气和乙烯回收率达到90%。     

Novel design of composite generally weighted moving average and cumulative sum charts

The cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) charts are popular statistical tools to improve the performance of the Shewhart chart in detecting small process shifts. In this study, we propose the mixed generally weighted moving average (GWMA)‐CUSUM chart and its reverse‐order CUSUM‐GWMA chart to enhance detection ability compared with existing counterparts. The simulation revealed that the mixed GWMA‐CUSUM and mixed CUSUM‐GWMA charts have the sensitivity to detect small process shifts and efficient structures compared with the mixed EWMA‐CUSUM and mixed CUSUM‐EWMA charts, respectively. Moreover, the mixed GWMA‐CUSUM chart with a large design parameter has robust performance, regardless of the high tail t distribution or right skewness gamma distribution.     

Propagation characteristics of the ten-parameter family of partially coherent general anisotropic gaussian schellmodel (AGSM) beams passing through first-order optical system

Abstract

Based on the closed property of AGSM beams under the action of first-order optical systems, the explicit transformation and twist expressions for the principal axes of intensity distribution, transverse coherence distribution and the principal curvatures of phase front in the cross-spectral density function of AGSM beams are derived. For typical applications, for AGSM beams passing through free space, the twist and variation regularities of the principal axes and the principal curvatures are analysed in detail. The twist-free conditions are discussed and the twist influenced by the physical parameters of the incident beam analysed. It is shown from the analysis that the principal curvatures of phase front are not zero at the reference planes where any of the corresponding principal axes of the beam spot obtains its minimum, and the conditions where the principal curvatures are zero is discussed.     

箱梁表面的压力分布对颤振稳定性的影响EI北大核心CSCD

该文建立了箱梁表面压力与颤振导数之间的数学关系,探讨了表面压力的分布特性对箱梁颤振导数和颤振临界风速的影响。结合流固松耦合的计算方法,利用动网格技术模拟了箱梁的风致振动。采用分块分析方法研究了箱梁表面压力的局部特性对颤振导数以及系统振动能量的影响。研究结果表明:箱梁迎风侧风嘴附近的分布压力对模型振动的稳定性产生了不利的影响,而模型尾部的压力则有助于提高系统的颤振临界风速。当迎风侧的分布压力向模型尾部移动时,对箱梁颤振稳定性影响较大的颤振导数则会发生较显著的变化,箱梁的颤振临界风速也随之增加,因此断面迎风侧风嘴附近区域的分布压力对颤振导数和系统振动的稳定性影响最大。另外,迎风侧风嘴附近的区域也是振动系统吸收气动能量的主要部位,而箱梁尾部风嘴附近的区域则消耗系统的振动能量。箱梁表面压力与模型振动最大位移之间的相位差对颤振导数有较大影响,当相位差沿断面呈反对称分布,并使气动阻尼始终为负时,则有利于箱梁颤振的稳定性。     

基于ProCAST的ZL114A尾段壳体凝固成形数值模拟与工艺优化

目的 针对ZL114A尾段壳体研制需求,利用低压充型液态成形工艺与数值仿真计算,预测疏松缺陷分布位置及严重程度,通过改进工艺来减少疏松缺陷,进而提高生产合格率。方法 基于Pro CAST软件对ZL114A尾段壳体低压充型凝固过程进行仿真计算,分析充型凝固过程中的流动场与温度场分布、充型时间、流动长度与凝固时间,预测疏松缺陷分布位置及严重程度,结合枝晶相干点双电偶热分析法测试结果,对低压充型工艺进行设计优化。结果 由尾段壳体凝固疏松缺陷的仿真计算结果与枝晶相干点温度测试结果可知,低压充型增压速度得到提高,保压时间有所延长,对安装凸台冷铁材质与厚度进行设计优化后,疏松缺陷得到显著改善。结论 通过数值仿真计算指导了铸造工艺设计,制备得到了满足技术指标要求的ZL114A尾段壳体。