Abstract
Quantile estimates of the annual maximum distribution can be obtained by fitting theoretical distributions to the maxima in separate seasons, e.g. to the monthly maxima. In this paper, asymptotic expressions for the bias and the variance of such estimates are derived for the case that the seasonal maxima follow a Gumbel distribution. Results from these expressions are presented for a situation with no seasonal variation and for maximum precipitation depths at Uccle/Ukkel (Belgium). It is shown that the bias is often negligible and that the variance reduction by using seasonal maxima instead of just the annual maxima strongly depends on the seasonal variation in the data. A comparison is made between the asymptotic standard error of quantile estimates from monthlymaxima with those from a partial duration series. Much attention is paid to the effect of model misspecification on the resulting quantile estimates of the annual maximum distribution. The use of seasonal maxima should be viewed with caution when the upper tail of this distribution is of interest.
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Buishand, T.A., Demaré, G.R. Estimation of the annual maximum distribution from samples of maxima in separate seasons. Stochastic Hydrol Hydraul 4, 89–103 (1990). https://doi.org/10.1007/BF01543284
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DOI: https://doi.org/10.1007/BF01543284