一个组合分布模型及其参数估计

本文根据极值分布理论,提出了一个由原始分布和尾分布组成的组合分布模型,研究了组合分布模型中原始分布和尾分布的确定方法,建立了组合分布模型参数估计的加权最优化模型,实例计算说明,组合分布较好地反映了风险变量极值事件的风险。     

基于正则逆Gamma分布和广义极值分布的VaR计算

股指收益率的分布和风险价值(VaR)的计算是证券市场研究的热点问题.本文对来自上证指数和深证成指日收益率采用正则逆Gamma分布和偏T分布(SST)分别进行拟合,对极值序列(周、月极大值和极小值)建立广义极值分布函数。并由此计算VaR值,度量这几种序列的风险价值.结果表明正则逆Gamma分布能更好地拟合日收益率的分布,以及采用周极值收益率的广义极值分布计算VaR值来估计风险较为合理.     

关于Hsler-Reiss分布的一点注记

本文研究了服从二元二项分布的随机向量序列的极值分布问题.利用构造性的方法,证明了服从二元二项分布的随机向量序列之极值依分布收敛到Hsler-Reiss 分布, 将已有结论推广到离散情形.     

A NOTE ON H(U)SLER-REISS DISTRIBUTION

本文研究了服从二元二项分布的随机向量序列的极值分布问题.利用构造性的方法,证明了服从二元二项分布的随机向量序列之极值依分布收敛到Hüsler-Reiss分布,将已有结论推广到离散情形.     

Box-Cox正态分布及其在降雨极值分析中的应用

Box-Cox变换和正态分布有机结合构建新的Box-Cox正态分布,可以用来研究降水极值分布拟合问题,采用极大似然估计方法估计Box-CoX正态分布的参数,并基于1951-2010年河北省21个气象站逐日降水观测资料,拟合逐年日最大降水量序列,借助K-S与A-D方法进行拟合优度的比较,结果表明BoX-Cox正态分布能适应不同站点的降雨极值分布的拟合,且大部分优于降雨极值分布拟合中常用的广义极值(GEV)分布、Weibull分布、Gamma分布,因而对掌握降雨极值分布规律,分析降水极值重现期、时空特征和变化趋势具有重要意义。     

二元极值混合模型相关结构的研究

二元极值混合模型由于不能反映极值变量之间的完全相关性,因而在应用上受到了一定的限制,但对适当的相关性仍是一个很好的模型.本文给出了二元极值混合模型的一些基本性质,特别用随机模拟方法研究了对来自其它不同极值copula的随机样本,用混合模型拟合可能产生的影响. 结果表明,如果以Kendallτ表示变量间的相关性,在一定范围内,混合模型能够很好的反映其它模型所具有的相关性,且对渐近独立模型边际参数估计的偏差也不太大.最后应用混合条件分布与GEV条件分布分析英镑对美元和英镑对加元两支汇率日对数回报收益率的风险相关性.     

汽车交通事故损失分布的尾部估计

由于巨额损失对保险公司的影响非常大,费率厘定过程中对极值分布的研究非常重视。本文从极值理论的角度出发,以上海市虹口区2003年的汽车交通事故损失数据为样本,探讨了损失分布的尾部估计方法,并利用该地区2006年的汽车交通事故损失对结论进行了验证。研究结果发现,广义帕雷托分布确实对损失额的尾部提供了较好的拟合,但这依赖于门槛值的恰当选择。传统的门槛值选择方法主观性较强,而通过重复多次的交叉验证技巧,我们可以估计广义帕雷托分布的最合适门槛值位置。     

非寿险中巨额损失数据的拟合与精算

利用极值理论给出了一种新的解决非寿险精算中巨额损失保费厘定问题的方法。在建模过程首先给出了极值理论的最大吸引域检验问题,然后利用不同方法讨论了最优门限值的选取问题,并在POT模型下利用广义帕累托分布对巨额损失分布进行拟合。然后在假设损失次数服从泊松分布的条件下,在复合泊松分布的框架下讨论了险位超赔再保险的纯保费计算问题。     

极值分布和威布尔分布异常数据的检验方法

本文对威布尔分布的极值分布异常数据的检验给出了一系列的方法，首先，导入了极值分布下一般Ｄｉｘｏｎ型统计量的精确分布，同时还给出了改进的Ｇ型统计量，及它们的分位点表。最后本文提出了一个新的统计量；Ｆ型统计量，并用Ｍｏｎｔｅ－Ｃａｒｌｏ模拟的方法给出其分位点表，从而首次给出威布尔分布异常值的直接检验方法。本文进一步讨论了这些检验方法的功效，且表明Ｆ型检验是最优的。     

多个独立同分布应力作用下的极值型─极值型(Ⅰ-Ⅲ)模式的结构可靠性估计

本文讨论了在多个独立同分布应力作用下的极值型－极值型（Ⅰ－Ⅲ）模式结构可靠性估计，给出了分布参数及结构可靠度的短估计．极大似然估计及量信下限．     

一种均匀分布的修正分布——UR-n分布

从现实应用中 ,提出一种均匀分布的修正分布 ,并进一步研究了n次修正分布———UR n分布的性质及其极限性质 .这一分布在军事中武器精度的研究、天文观测等多方面都很有利用价值 .     

非线性飘移布朗运动的极值分布

本文研究了从x出发的非线性漂移布朗运动的极大值、极小值和首达时问题.利用测度变换以及布朗运动的一些重要性质,如反射原理,增量的独立性等,获得了两种极值分布函数的精确表达式,得到了首达时的分布函数.结果表明,线性漂移布朗运动的极大值极小值以及首达时的分布问题的有关结果是本文结论的推论,最后给出一个例子.     

Testing the Gumbel Hypothesis Via the Pot-Method

We consider an i.i.d. sample, generated by some distribution function, which belongs to the domain of attraction of an extreme value distribution with unknown shape and scale parameters. We treat the scale parameter as a nuisance parameter and establish for the hypothesis of Gumbel domain of attraction an asymptotically optimal test based on those observations among the sample, which exceed a given threshold sequence. Asymptotic optimality is achieved along certain contiguous extreme value alternatives within the concept of local asymptotic normality (LAN). Adaptive test procedures exist under restrictive assumptions. The finite sample size behavior of the proposed test is studied by simulations and it is compared to that of a test based on the sample coefficient of variation.     

Random Features of the Fatigue Limit

The classical fatigue limit is often an important characteristic in fatigue design regarding metallic material. The limit is usually obtained from a staircase test in combination with some assumption about the statistical distribution of the limit. This distribution can be of a normal, log-normal or of extreme value type and no particular physical argument gives favor to any specific distribution. This leads to a certain ambiguity in the evaluation of test results which forces the designer to introduce large safety factors. In order to find a physically based statistical distribution for use in staircase tests to determine the fatigue limit we present here a random model for the fatigue limit based on the following assumptions; (i) The square root area model according to Murakami and co-workers is valid, (ii) the randomness in the fatigue limit is induced by the randomness of the maximum defect size, (iii) the random maximum defect size has an extreme value distribution of Gumbel type. This leads to the fatigue limit distribution based on Gumbel (FLG), which is recommended to replace the normal distribution in the evaluation of staircase fatigue tests in case of hard materials. It turns out that the skewness of the resulting distribution depends on the coefficient of variation; with a normal-like non-skewed distribution at the coefficient of variation of five percent.     

On the limiting joint distribution of the extreme order statistics

The connection between extreme values and record-low values is exploited to derive simply the limiting joint distribution of the r largest order statistics. The use of this distribution in the modelling of corrosion phenomena is considered, and the extrapolation of maxima in space and time is described in this context. There has been recent emphasis on movement away from classical extreme value theory to more efficient estimation procedures. This shift is continued with the illustration of the extra precision of predicted maxima obtained from a model based on extreme order statistics over the classical extreme value approach.     

二项-广义Pareto复合极值分布模型的统计推断

极值理论主要研究小概率、大影响的极端事件.当前,复合极值分布已经广泛应用于水文、气象、地震、保险、金融等领域.本文以极值类型定理和PBDH定理为理论依据,构建了二项-广义Pareto复合极值分布模型;使用概率加权矩方法,对所建立的复合模型推导参数估计式;利用计算机模拟,得到了Kolmogorov-Smirnov(简称KS)检验统计量的临界值.     

Comparing extreme models when the sign of the extreme value index is known

In the literature on analyzing extremes, both generalized Pareto distributions and Pareto distributions are employed to infer the tail of a distribution with a known positive extreme value index. Similar studies exist for a known negative extreme value index. Intuitively, one should not employ the generalized Pareto distribution in the case of knowing the sign of the extreme value index. In this work, we show that fitting a generalized Pareto distribution is equivalent to the model in Hall (1982) in the case of a negative extreme value index, in both improving the rate of convergence and including the bias term of the asymptotic results of that reference. When the extreme value index is known to be positive, we show that fitting a generalized Pareto distribution may be preferred in some cases determined by a so-called second-order parameter and the extreme value index itself.     

MULTIVARIATE EXTREME VALUE DISTRIBUTION AND ITS FISHER INFORMATION MATRIX

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Asymptotic expansions of the moments of extremes from general error distribution

In this paper, we derive the asymptotic expansions of the moments of normalized partial maxima for general error distribution. A byproduct is to deduce the convergence rates of the moments of normalized maxima to the moments of the corresponding extreme value distribution.