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| Titel |
The Gumbel hypothesis test for left censored observations using regional earthquake records as an example |
| VerfasserIn |
E. M. Thompson, J. B. Hewlett, L. G. Baise, R. M. Vogel |
| Medientyp |
Artikel
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| Sprache |
Englisch
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| ISSN |
1561-8633
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| Digitales Dokument |
URL |
| Erschienen |
In: Natural Hazards and Earth System Science ; 11, no. 1 ; Nr. 11, no. 1 (2011-01-11), S.115-126 |
| Datensatznummer |
250009041
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| Publikation (Nr.) |
 copernicus.org/nhess-11-115-2011.pdf |
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| Zusammenfassung |
| Annual maximum (AM) time series are incomplete (i.e., censored) when no
events are included above the assumed censoring threshold (i.e., magnitude of
completeness). We introduce a distrtibutional hypothesis test for
left-censored Gumbel observations based on the probability plot correlation
coefficient (PPCC). Critical values of the PPCC hypothesis test statistic
are computed from Monte-Carlo simulations and are a function of sample size,
censoring level, and significance level. When applied to a global catalog of
earthquake observations, the left-censored Gumbel PPCC tests are unable to
reject the Gumbel hypothesis for 45 of 46 seismic regions. We apply four
different field significance tests for combining individual tests into a
collective hypothesis test. None of the field significance tests are able to
reject the global hypothesis that AM earthquake magnitudes arise from a
Gumbel distribution. Because the field significance levels are not
conclusive, we also compute the likelihood that these field significance
tests are unable to reject the Gumbel model when the samples arise from a
more complex distributional alternative. A power study documents that the
censored Gumbel PPCC test is unable to reject some important and viable
Generalized Extreme Value (GEV) alternatives. Thus, we cannot rule out the
possibility that the global AM earthquake time series could arise from a GEV
distribution with a finite upper bound, also known as a reverse Weibull
distribution. Our power study also indicates that the binomial and uniform
field significance tests are substantially more powerful than the more
commonly used Bonferonni and false discovery rate multiple comparison
procedures. |
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