Abstract
This paper discusses the characteristics of quantile and its standard deviation estimated by applying an MLM (maximum likelihood method) -based extreme value analysis model to various kinds of annual maximum data samples with historical information. The samples of storm surge height, flood, sea level height and lake level height are acquired from published papers. An optimum distribution is selected from a family of candidate distributions such as the Gumbel, GEV and Weibull distributions according to an MLL (maximum log-likelihood) criterion. Main findings are as follows; 1) The model yields steadily reasonable estimates of quantile and its standard deviation even in the cases of samples including historical information. 2) Introduction of historical information in the extreme value analysis may contribute to a reduction of the standard deviation, that is the improvement of a statistical reliability of the estimated quantile, in cases where a proper evaluation of historical information is critical.
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