Second order regular variation and its applications to rates of convergence in extreme-value distribution

Fuming Lin; Zuoxiang Peng; Saralees Nadarajah

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Second order regular variation and its applications to rates of convergence in extreme-value distribution

机译：二阶正则变化及其在极值分布收敛速度中的应用

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The rate of convergence of the distribution of order statistics to the corresponding extreme-value distribution may be characterized by the uniform and total variation metrics. de Haan and Resnick [4] derived the convergence rate when the second order generalized regularly varying function has second order derivatives. In this paper, based on the properties of the generalized regular variation and the second order generalized variation and characterized by uniform and total variation metrics, the convergence rates of the distribution of the largest order statistic are obtained under weaker conditions.

机译：订单统计信息的分布与相应的极值分布的收敛速度可以用统一和总体变化量度来表征。当二阶广义规则变化函数具有二阶导数时，de Haan和Resnick [4]推导收敛速度。本文基于广义正则变异和二阶广义变异的性质，并以统一和总变异度量为特征，在弱条件下获得了最大阶统计量分布的收敛速度。

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《Bulletin of the Korean Mathematical Society》 |2008年第1期|共20页
作者
Fuming Lin; Zuoxiang Peng; Saralees Nadarajah;
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中图分类数学;
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机译：极值理论中的二阶正态变化和收敛速度
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3. Fundamental roles of extreme-value distributions in dielectric breakdown and memory applications (minimum-value versus maximum-value statistics) [J] . Wu Ernest, Ando Takashi, Li Baozhen, Japanese journal of applied physics . 2020,第SM期

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4. Regular variation, Paretian distributions, and the interplay of light and heavy tails in the fractality of asymptotic models [C] . Dinis D. Pestana, Sandra M. Aleixo, J. Leonel Rocha International Conference on Chaotic Modeling, Simulation, and Applications . 2011

机译：常规变化，帕氏菌分布，以及渐近模型的断裂中的轻质和重物的相互作用
5. On Limiting Distributions and Convergence Rates of Random Processes over Discrete Structures [D] . Ozdemir, Alperen. 2020

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6. Random distributions of initial porosity trigger regular necking patterns at high strain rates [O] . K. E. N’souglo, A. Srivastava, S. Osovski, -1

机译：初始孔隙率的随机分布会在高应变速率下触发规则的颈缩模式
7. Second-Order Regular Variation and Rates of Convergence in Extreme-Value Theory [O] . de Haan, L., Resnick, S. 1993

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8. Results on Statistical Estimation and Hypothesis Testing with Application to the Weibull and Extreme-Value Distributions [R] . Mann, N. R. 1968

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Second order regular variation and its applications to rates of convergence in extreme-value distribution

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