The maximum size of the planar sections of random spheres and its application to metallurgy

A theorem of this paper proves that if the size distribution of random spheres is generalized gamma, its Wicksell transform and other related distributions belong to the domain of attraction of the Gumbel distribution. The theorem also shows the attraction coefficients of the distributions. The fatigue strength of high-strength steel is closely related to the maximum size of nonmetallic inclusions in the region of maximum stress of the steel. Murakami and others developed a method, making use of the Gumbel QQ-plot, for predicting the maximum size from the size distribution of inclusion circles in microscopic view-fields. Based on the Gumbel approximation of the maximum of wicksell transforms, a modified and extended version of Murakami's method is justified, and its performance is evaluated by simulation.     

Extreme points of Banach lattices related to conditional expectations

Let (X,F,μ) be a complete probability space, B a sub-σ-algebra, and Φ the probabilistic conditional expectation operator determined by B. Let K be the Banach lattice {f∈L¹(X,F,μ):‖Φ(|f|)_‖∞<∞} with the norm ‖f‖=‖Φ(|f|)_‖∞. We prove the following theorems:

(1)

The closed unit ball of K contains an extreme point if and only if there is a localizing set E for B such that supp(Φ(χE))=X.

(2)

Suppose that there is n∈N such that f?nΦ(f) for all positive f in L^∞(X,F,μ). Then K has the uniformly λ-property and every element f in the complex K with is a convex combination of at most 2n extreme points in the closed unit ball of K.

     

Software for the analysis of extreme events: The current state and future directions

The last few years have seen a significant increase in publicly available software specifically targeted to the analysis of extreme values. This reflects the increase in the use of extreme value methodology by the general statistical community. The software that is available for the analysis of extremes has evolved in essentially independent units, with most forming extensions of larger software environments. An inevitable consequence is that these units are spread about the statistical landscape. Scientists seeking to apply extreme value methods must spend considerable time and effort in determining whether the currently available software can be usefully applied to a given problem. We attempt to simplify this process by reviewing the current state, and suggest future approaches for software development. These suggestions aim to provide a basis for an initiative leading to the successful creation and distribution of a flexible and extensible set of tools for extreme value practitioners and researchers alike. In particular, we propose a collaborative framework for which cooperation between developers is of fundamental importance. AMS 2000 Subject Classification Primary—62P99     

On the use of alumina in HPLC with aqueous mobile phases at extreme pH

Summary The applicability of alumina as a stationary phase in liquid chromatography is considered. Despite the presence of hydroxyl groups on wetted alumina, chemical modification with silanes by analogy to silica is not successful. Although depolarisation can be achieved with hexamethyldisilazane, the product is not stable to hydrolysis in aqueous media. The use of alumina as an ion-exchanger is more promising, especially because alumina appears to be stable over a very broad pH range. As a result of its amphoteric character alumina can be used either as an anion-exchanger or as a cation-exchanger. The latter possibility is more profitable in alkaline solvents and allows the separation of strongly basic compounds at pH values as high as 12. Retention can be controlled by judicious choice of ionic strength, counter ion and pH.     

极紫外光刻系统物镜光学元件的支撑与分析

介绍了极紫外光刻系统物镜光学元件的支撑原理和支撑要求,分析了符合运动学支撑要求的物镜支撑结构和面形检测用支撑结构;针对支撑结构性能和支撑方案中关键问题进行了深入研究,并提出了相应的解决方案。最后建立了支撑结构的有限元模型,并在此基础上进行了重力场中的镜体变形分析和温度场作用下系统的热变形分析。分析结果表明,检测用支撑与实际用支撑两种结构在重力环境下支撑出的元件面形基本相同,面形相差0.0026nm(RMS);温控范围为0.05℃时,由机械结构热变形引起的镜体面形变化在0.001nm(RMS)量级。研究结果表明,运动学物镜元件支撑结构能够满足极紫外光刻系统对于物镜机械支撑结构的要求。     

用近红外无损肌氧及运动心率检测技术评定100m极量强度运动对心脏冲击影响

利用连续双波长近红外光技术测量肌肉中血红蛋白含氧量的变化情况,同时应用运动心率无线实时采集设备,设计了检测实时肌肉组织血氧含量和瞬时心率实验方案,对6名健康男性进行了100 m跑同步实测实验。实验表明,肌肉组织氧合血红蛋白浓度在100 m跑结束后继续降低,达到最低值的时刻滞后于运动结束时刻的时间为(6.65±1.10)s;心率则在运动结束后继续上升,达到最高值的时刻滞后于运动结束时刻的时间为(8.00±1.57)s。这些结果显示了双波长近红外光组织氧测试技术和运动心率无线实时采集系统能够正确检测极量强度运动时的血氧参数和心率,揭示了极量强度运动过程中肌肉中氧运输与消耗的过程及其与心率之间的动力学特征。     

Distributionally robust inference for extreme Value-at-Risk

Under general multivariate regular variation conditions, the extreme Value-at-Risk of a portfolio can be expressed as an integral of a known kernel with respect to a generally unknown spectral measure supported on the unit simplex. The estimation of the spectral measure is challenging in practice and virtually impossible in high dimensions. This motivates the problem studied in this work, which is to find universal lower and upper bounds of the extreme Value-at-Risk under practically estimable constraints. That is, we study the infimum and supremum of the extreme Value-at-Risk functional, over the infinite dimensional space of all possible spectral measures that meet a finite set of constraints. We focus on extremal coefficient constraints, which are popular and easy to interpret in practice. Our contributions are twofold. First, we show that optimization problems over an infinite dimensional space of spectral measures are in fact dual problems to linear semi-infinite programs (LSIPs) – linear optimization problems in Euclidean space with an uncountable set of linear constraints. This allows us to prove that the optimal solutions are in fact attained by discrete spectral measures supported on finitely many atoms. Second, in the case of balanced portfolia, we establish further structural results for the lower bounds as well as closed form solutions for both the lower- and upper-bounds of extreme Value-at-Risk in the special case of a single extremal coefficient constraint. The solutions unveil important connections to the Tawn–Molchanov max-stable models. The results are illustrated with two applications: a real data example and closed-form formulae in a market plus sectors framework.     

Modelling life tables with advanced ages: An extreme value theory approach

We propose a new model – we call it a smoothed threshold life table (STLT) model – to generate life tables incorporating information on advanced ages. Our method allows a smooth mortality transition from non-extreme to extreme ages, and provides objectively determined highest attained ages with which to close the life table.We proceed by modifying the threshold life table (TLT) model developed by Li et al. (2008). In the TLT model, extreme value theory (EVT) is used to make optimal use of the relatively small number of observations at high ages, while the traditional Gompertz distribution is assumed for earlier ages. Our novel contribution is to constrain the hazard function of the two-part lifetime distribution to be continuous at the changeover point between the Gompertz and EVT models. This simple but far-reaching modification not only guarantees a smooth transition from non-extreme to extreme ages, but also provides a better and more robust fit than the TLT model when applied to a high quality Netherlands dataset. We show that the STLT model also compares favourably with other existing methods, including the Gompertz–Makeham model, logistic models, Heligman–Pollard model and Coale–Kisker method, and that a further generalisation, a time-dependent dynamic smooth threshold life table (DSTLT) model, generally has superior in-sample fitting as well as better out-of-sample forecasting performance, compared, for example, with the Cairns et al. (2006) model.     

折现的未决赔款准备金估计的随机逼近

凸序意义下的随机界是估计具有相依性随机变量和分布的良好工具.在考虑货币时间价值的基础上,通过随机上下界的两种不同形式的凸组合对未决赔款准备金的估计进行逼近,并通过矩匹配法,给出了最优权数的计算公式.通过一个实例对所述方法进行验证.     

Asymptotics of discounted aggregate claims for renewal risk model with risky investment

Under the assumption that the claim size is subexponentially distributed and the insurance surplus is totally invested in risky asset, a simple asymptotic relation of tail probability of discounted aggregate claims for renewal risk model within finite horizon is obtained. The result extends the corresponding conclusions of related references.