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MLM-Based Extreme Value Analysis Model for Censored Sample and Its Applicability

Author(s): M. Yamaguchi; Y. Hatada; H. Nonaka

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Keywords: Extreme value analysis; Censored sample; Maximum likelihood estimate; Monte-Carlo simulation; Gumbel; Weibull and GEV distributions; Measurement dat

Abstract: A large scale Monte-Carlo simulation is conducted to investigate the availability of an extreme value analysis model with aid of a jackknife method for a censored annual maxima (AM) sample, in which the maximum likelihood method (MLM) is applied for estimation of the parameters in either of the Gumbel, Weibull and GEV distributions used as the candidate distributions. Then, the MLM-based model is applied to a year-long measurement AM sample with partly missing data to evaluate the return value and its confidence level. The simulation results indicate that the MLM-based model with aid of a jackknife correction or the observed information matrix (OIM) method may yield proper estimates of return value and its squrare-root variance (SRV) in the cases of the 2-parameter distribution such as the Gumbel distribution or either of the shape parameter-fixed Weibull and GEV distributions, while it may not always give satisfactory estimates for samples with lesser size in the cases of the 3-parameter distribution such as either of the original Weibull and GEV distributions. Analysis using the measurement AM sample with missing data reveals that the effect of data censoring on the estimates of return value and its SRV is generally significant. Also, it is shown that the MLM-based estimate is statistically more efficient than the LSM (least square method) -based estimate.


Year: 2003

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