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 - , 2016, Abstract: 【目的】研究并建立广义极值分布无偏经验概率计算公式，为广义极值分布经验概率的计算提供支持。【方法】应用次序统计量原理，推导广义极值分布无偏经验概率计算公式，采用统计试验方法将推导的公式与现有的经验频率公式进行对比，对其进行检验，最后以陕北地区12个水文测站的年最大洪峰流量系列为例进行模型应用。【结果】推导出了便于工程设计应用的广义极值分布经验概率计算公式GEVQG。统计试验和实例应用表明：推导的公式GEVQG和现有经验频率公式Cunnane公式的相对误差和偏差均较小，并且对研究区的拟合效果良好。【结论】推导的计算公式GEVQG和Cunnane公式均可以作为广义极值分布经验概率计算的优选公式，为工程水文经验概率计算提供了新的选择。【Objective】This study developed the unbiased plotting position formula for general extreme value (GEV) distribution.【Method】Based on the theory of order statistics,this paper developed an unbiased plotting position formula for the GEV distribution.The statistical testing was used to compare the developed formula and other existing formulas.At last,the parameters of annual maximum floods peak flow series of twelve stations in Northern Shaanxi were estimated.【Result】This paper developed a practical and convenient plotting position formula for the GEV distribution.The case study and statistical testing showed that the developed formula and Cunnane formula had small error and bias as well as good fitness in the study area.【Conclusion】The developed formula and Cunnane formula can be used as better methods for the GEV distribution,which provides new choice for empirical probability calculation in hydrology engineering
 腐蚀科学与防护技术 , 2008, Abstract: Corrosion depth data of partial backwash pipes of a sea water system in nuclear power plant was treated statistically using the extreme value probability distribution i.e.the so called Gumbel distribution.And the maximum corrosion depth 10.8±1.3 mm of the whole backwash pipes had been predicted with the return period which equals to 149.The corrosion depth data were subjected to Gumbel distribution treatment and the parameters of its probability function were estimated by MVLUE method.The Gumbel probability distribution was checked by Kolmogorov-Smirnov test and proved to be accurate.As a result,the maximum depth predicted by it was confident.
 Statistics , 2008, DOI: 10.1088/1742-5468/2008/05/P05004 Abstract: We study the factorised steady state of a general class of mass transport models in which mass, a conserved quantity, is transferred stochastically between sites. Condensation in such models is exhibited when above a critical mass density the marginal distribution for the mass at a single site develops a bump, $p_{\rm cond}(m)$, at large mass $m$. This bump corresponds to a condensate site carrying a finite fraction of the mass in the system. Here, we study the condensation transition from a different aspect, that of extreme value statistics. We consider the cumulative distribution of the largest mass in the system and compute its asymptotic behaviour. We show 3 distinct behaviours: at subcritical densities the distribution is Gumbel; at the critical density the distribution is Fr\'echet, and above the critical density a different distribution emerges. We relate $p_{\rm cond}(m)$ to the probability density of the largest mass in the system.
 Physics , 2014, DOI: 10.3390/e16105523 Abstract: We study the extreme value distribution of stochastic processes modeled by superstatistics. Classical extreme value theory asserts that (under mild asymptotic independence assumptions) only three possible limit distributions are possible, namely: Gumbel, Fr\'echet and Weibull distribution. On the other hand, superstatistics contains three important universality classes, namely $\chi^2$-superstatistics, inverse $\chi^2$-superstatistics, and lognormal superstatistics, all maximizing different effective entropy measures. We investigate how the three classes of extreme value theory are related to the three classes of superstatistics. We show that for any superstatistical process whose local equilibrium distribution does not live on a finite support, the Weibull distribution cannot occur. Under the above mild asymptotic independence assumptions, we also show that $\chi^2$-superstatistics generally leads an extreme value statistics described by a Fr\'echet distribution, whereas inverse $\chi^2$-superstatistics, as well as lognormal superstatistics, lead to an extreme value statistics associated with the Gumbel distribution.