On the joint distribution of the largest flood and its time of occurrence

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Abstract
In a partial duration series the total number of exceedances as well as the exceedance flows is formalized as a random sequence of random variables. This formalism along with some physically reasonable assumptions leads to a rigorous expression for the joint distribution function of the largest exceedance and its time of occurrence. The deviation provides one way to consider the temporal changes in the occurrence and the magnitudes of individual exceedances due to ‘seasonal’ influences. This approach is general enough to be applied to any time interval of interest; furthermore, the derived expressions are exact (nonasymptotic). It may thus represent an improvement over an application of Gumbel's classical extreme value theory to flood phenomena, which is based on the premise that a large number of exceedances are available over time intervals of interest and which provides only asymptotic expressions.

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