A generalization of the Nataf transformation to distributions with elliptical copula

被引：123

作者：

Lebrun, Regis ^{[1
]}

Dutfoy, Anne ^{[2
]}

机构：

[1] EADS Innovat Works, F-92152 Suresnes, France

[2] EDF R&D, Ind Risk Management, F-92140 Clamart, France

来源：

PROBABILISTIC ENGINEERING MECHANICS | 2009年 / 24卷 / 02期

关键词：

Nataf transformation; Elliptical copula; FORM; SORM; Breitung's approximation;

D O I：

10.1016/j.probengmech.2008.05.001

中图分类号：

TH [机械、仪表工业];

学科分类号：

0802 ;

摘要：

In the first article [Lebrun R, Dutfoy A. An innovating viewpoint of the isoprobabilistic Nataf transformation with the copula theory within exceedance threshold uncertainty analysis. Probabilistic Structure Engineering Structural Reliability. 2008 [in press]], we showed that the Nataf transformation is a way to model the dependence structure of a random vector by a normal copula, parameterized by its correlation matrix. Following this analysis, we propose an extension of this transformation to any elliptical copula, and give the equivalent of the First Order Reliability Method (FORM) and the Second Order Reliability Method (SORM) for this generalization. In particular, we derive the Breitung asymptotic approximation in this new context. (C) 2008 Elsevier Ltd. All rights reserved.

引用

页码：172 / 178

页数：7

共 17 条

[1]

[Anonymous], J ENG MECH-ASCE, DOI DOI 10.1061/(ASCE)0733-9399(1986)112:1(85)

[2]

ARNOLD SF, 1982, J ROY STAT SOC B MET, V44, P49

[3] ASYMPTOTIC APPROXIMATIONS FOR MULTINORMAL INTEGRALS [J].

BREITUNG, K .

JOURNAL OF ENGINEERING MECHANICS-ASCE, 1984, 110 (03) :357-366

[4]

DERKIUREGHIAN A, 1986, PROBALISTIC ENG MECH, V1, P105

[5]

DUTFOY A, ESREL 2007 C

[6]

EMBRECHTS P, 2001, MODELLING DEPENDANCE

[7]

HASOFER AM, 1974, J ENG MECH DIV-ASCE, V100, P111

[8]

Joe H., 1997, MULTIVARIATE MODELS

[9]

KOTZ KT, 1987, SYMMETRIC MULTIVARIA

[10]

LEBRUN R, 2004, P 8 INT C PROB SAF A

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