Extreme value theory in mixture distributions and a statistical method to control the possible bias

Wonseon Gwak; Hyein Goo; Yang Ho Choi; Jae Youn Ahn

doi:10.1016/j.jkss.2016.04.003

Extreme value theory in mixture distributions and a statistical method to control the possible bias

Wonseon Gwak, Hyein Goo, Yang Ho Choi, Jae Youn Ahn

Department of Statistics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

In this paper, extreme behaviors of a mixture distribution are analyzed. We investigate some cases where the mixture distributions are in the proper domain of attraction so that the extreme value of mixture distributions converges to the proper Generalized Extreme Value distribution (GEV). However, in general, there is no guarantee that the distribution of the data is in the proper maximum domain of attraction. Furthermore, since the convergence rate can be slow even with guaranteed asymptotic convergence, GEV estimation method might provide a biased estimation, as shown in Choi et al. (2014). The paper provides a safe method to control the quality of the quantile estimator in extreme values.

Original language	English
Pages (from-to)	581-594
Number of pages	14
Journal	Journal of the Korean Statistical Society
Volume	45
Issue number	4
DOIs	https://doi.org/10.1016/j.jkss.2016.04.003
State	Published - 1 Dec 2016

Bibliographical note

Funding Information:
For Jae Youn Ahn, this work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korean Government ( 2013R1A1A1076062 ).

Publisher Copyright:
© 2016 The Korean Statistical Society

Keywords

Extreme behavior
Generalized Extreme distribution
Mixture distribution
Precipitation

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10.1016/j.jkss.2016.04.003

Cite this

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title = "Extreme value theory in mixture distributions and a statistical method to control the possible bias",

abstract = "In this paper, extreme behaviors of a mixture distribution are analyzed. We investigate some cases where the mixture distributions are in the proper domain of attraction so that the extreme value of mixture distributions converges to the proper Generalized Extreme Value distribution (GEV). However, in general, there is no guarantee that the distribution of the data is in the proper maximum domain of attraction. Furthermore, since the convergence rate can be slow even with guaranteed asymptotic convergence, GEV estimation method might provide a biased estimation, as shown in Choi et al. (2014). The paper provides a safe method to control the quality of the quantile estimator in extreme values.",

keywords = "Extreme behavior, Generalized Extreme distribution, Mixture distribution, Precipitation",

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note = "Funding Information: For Jae Youn Ahn, this work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korean Government ( 2013R1A1A1076062 ). Publisher Copyright: {\textcopyright} 2016 The Korean Statistical Society",

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AU - Choi, Yang Ho

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N1 - Funding Information: For Jae Youn Ahn, this work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korean Government ( 2013R1A1A1076062 ). Publisher Copyright: © 2016 The Korean Statistical Society

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Extreme value theory in mixture distributions and a statistical method to control the possible bias

Abstract

Bibliographical note

Keywords

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