Robust estimators and tests for bivariate copulas based on likelihood depth

Estimators and tests based on likelihood depth for one-parametric copulas are given. For the Gaussian and Gumbel copulas, it is shown that the maximum depth estimators are biased. They can be corrected and the new estimators are robust against contamination. For testing, simplicial likelihood depth is considered. Because of the bias of the maximum depth estimator, simplicial likelihood depth is not a degenerated U-statistic so that easily asymptotic α-level tests can be derived for arbitrary hypotheses. Tests are in particular investigated for the one-sided alternatives. Simulation studies for the Gaussian and Gumbel copulas show that the power of the first test is rather good, but the latter one has to be improved, which is also done here. The new tests are robust against contamination.     

A phase-field model of 2D grain size distribution in ceramics

Normal grain growth is a ubiquitous process in nature playing a central role in many technological applications of materials. Despite the considerable effort devoted to account for its features over the past years, there remain important aspects which are not fully understood. Among them, the mere existence of a grain distribution function for normal grain growth and its mathematical formulation deserves attention. Although it is commonly assumed that lognormal function is the “expected” grain distribution in materials, there are many examples, particularly in ceramics, in which such assumption has revealed to be not correct. An alternative grain size distribution is proposed after phase field model simulations of static and dynamic grain growth. A simple explanation based upon the local grain size correlation is proposed.     

基于Gumbel Copula函数的堆石坝沉降模型因子优选研究

为克服常规沉降模型因考虑众多影响因子造成欠拟合及预测精度不高的缺点,首先由因子优选准则得到沉降模型的预选因子集,运用了Copula熵和PMI(偏互信息)两种方法对预选因子集进行优选,再将优选因子集引入沉降模型并计算典型测点的沉降值,验证了该优选方法的可行性.实例表明,基于Gumbel函数的沉降模型拟合预测精度优于常规模...     

A comparison of historical land-use change patterns and recommendations for flood plain developments in three delta regions in Southeast Asia

Historical land-cover changes in three delta regions in Southeast Asia are assessed by using selected Landsat images from 1990 to 2005. Potential inundation areas of the delta regions for different return periods are estimated by using digital elevation model data and extreme-value distribution of annual maximum river discharges. The results indicate significant changes of natural land cover within the potential inundation areas due to agricultural exploitation and industrialization. Implications for flood-mitigation policies are discussed. There is a clear need for sustainable land-use management strategies in all three areas.     

A comparison of methods of extreme wind speed estimation

The paper presents a comparative assessment of methods for extreme value analysis of the US wind speed data using four different methods, namely Standard Gumbel, Modified Gumbel, Peaks-Over-Threshold (POT) and Method of Independent Storms (MIS). The analysis highlights the influence of methodological assumptions on the estimates of design wind speed corresponding to 50-year and 500-year return period. The results demonstrate that the MIS method leads to more stable quantile estimates than the POT method.     

A new direct version of the Cook-Mayne method for wind pressure probabilities in temperate storms

The original Cook-Mayne (CM) method for obtaining a wind pressure or load of a prescribed probability is reviewed. A new direct calculation method is introduced. This does not require either Monte Carlo simulations or the assumption that extreme pressures conform to the ultimate Fisher-Tippett Type I asymptote. The required value is calculated directly with no intermediate stages. The new method still relies on the original assumptions that both the pressure coefficient and the wind dynamic head have extremes which conform to the ultimate FT1 asymptote.Violation of these two assumptions is studied in some cases where calculations based on these assumptions are compared with exact results. The direct CM method is found to retain accuracy in spite of departures from the assumptions and therefore can provide a robust design tool.     

Reliability Evaluation of Phasor Measurement Unit: A System of Systems Approach

The phasor measurement unit has emerged as a complex, real-time measurement and control system necessitated by the modern power system, the most complex machinery. The extensive installation of phasor measurement units in recent times requires secure and reliable operation. The existing reliability models for phasor measurement unit reliability analysis are constrained by assumptions that disregard the inherent complexity, thus calling for the necessity of a system of systems engineering based reliability model for phasor measurement units. Such a system of systems engineering based model paves the way to accommodate different functional and logical relationships in a suitable way. Another major contribution of this article is the use of statistics of extremes to take into account the scarce failure data for phasor measurement units, which are recent in origin. The results reported in this article validate the efficacy of the system of systems engineering based reliability model.     

Probabilistic analysis of continuum damage mechanics of brittle materials

Uncertainty of material properties in solution of engineering problems is often a fundamental question. Statistical methods give a powerful tool for analysis of uncertainty. Monte Carlo simulations together with Gumbel distribution are used as a possible way to study influence of data dispersion on assessment of damage of brittle materials.     

基于Gumbel Copula的金融市场波动溢出模型

将Gumbel Copula函数与GARCH模型结合起来刻画金融市场间的尾部相关结构,结果表明,Gumbel Copula可以有效刻画金融市场波动溢出效应;对沪深股市的实证研究表明,次贷危机不仅造成了沪深股市的低迷,而且加剧了沪深股市的波动溢出效应,认为次贷危机是沪深股市相关结构的一个结构性变点.