Estimation of body and tail distribution under extreme events for reliability analysis

Woochul Lim, Tae Hee Lee, Seunghoon Kang, Su gil Cho

Research output: Contribution to journalArticle

Abstract

In the past decades, many reliability analyses have been developed and applied to engineering fields considering uncertainties of input and output random variables as normal distributions. However, when input uncertainty is taken into the system as extreme events such as weather, temperature, environmental conditions etc., output distribution cannot be described by normal distribution. On the other hand, one of distributions to analyze reliability of a system under extreme events is generalized Pareto distribution. Generalized Pareto distribution has been developed and applied for modelling extreme events. However, conventional methods estimate only the shape and scale parameters by assuming that the location parameter is chosen by experiences focused only on the tail distribution. However, since the tail distribution affected by the body distribution and vice versa, both the body and tail distributions should be considered when the parameters of distribution are estimated. In this study, therefore, a new parameter estimation method is proposed to determine shape, scale and location parameters simultaneously by combining likelihood functions of body and tail distributions using Akaike information criterion and generalized Pareto distribution, respectively. Finally, the parameters of body and tail distributions are estimated by maximum likelihood estimation. The proposed method is verified by using mathematical examples with and without inclusion of extreme events. Results show that the proposed method can estimate parameters and distributions for body and tail distributions as well as the more accurate reliability of system under extreme events.

Original languageEnglish
Pages (from-to)1631-1639
Number of pages9
JournalStructural and Multidisciplinary Optimization
Volume54
Issue number6
DOIs
StatePublished - 2016 Dec 1

Fingerprint

Extreme Events
Reliability Analysis
Reliability analysis
Tail
Normal distribution
Maximum likelihood estimation
Generalized Pareto Distribution
Random variables
Parameter estimation
Location Parameter
Shape Parameter
Scale Parameter
Gaussian distribution
Uncertainty
Akaike Information Criterion
Temperature
Output
Likelihood Function
Maximum Likelihood Estimation
Weather

Keywords

  • Akaike information criterion
  • Extreme events
  • Generalized Pareto distribution
  • Maximum likelihood estimation
  • Reliability analysis

Cite this

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title = "Estimation of body and tail distribution under extreme events for reliability analysis",
abstract = "In the past decades, many reliability analyses have been developed and applied to engineering fields considering uncertainties of input and output random variables as normal distributions. However, when input uncertainty is taken into the system as extreme events such as weather, temperature, environmental conditions etc., output distribution cannot be described by normal distribution. On the other hand, one of distributions to analyze reliability of a system under extreme events is generalized Pareto distribution. Generalized Pareto distribution has been developed and applied for modelling extreme events. However, conventional methods estimate only the shape and scale parameters by assuming that the location parameter is chosen by experiences focused only on the tail distribution. However, since the tail distribution affected by the body distribution and vice versa, both the body and tail distributions should be considered when the parameters of distribution are estimated. In this study, therefore, a new parameter estimation method is proposed to determine shape, scale and location parameters simultaneously by combining likelihood functions of body and tail distributions using Akaike information criterion and generalized Pareto distribution, respectively. Finally, the parameters of body and tail distributions are estimated by maximum likelihood estimation. The proposed method is verified by using mathematical examples with and without inclusion of extreme events. Results show that the proposed method can estimate parameters and distributions for body and tail distributions as well as the more accurate reliability of system under extreme events.",
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Estimation of body and tail distribution under extreme events for reliability analysis. / Lim, Woochul; Lee, Tae Hee; Kang, Seunghoon; Cho, Su gil.

In: Structural and Multidisciplinary Optimization, Vol. 54, No. 6, 01.12.2016, p. 1631-1639.

Research output: Contribution to journalArticle

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