Two‐Component Extreme Value Distribution for Flood Frequency Analysis

TLDR

Theoretical analysis of 39 Italian annual flood series indicates that the two‑component extreme value (TCEV) distribution, a member of the annual‑maximum compound Poisson family, can serve as a realistic parent flood distribution. The study proposes a more general TCEV model that treats each flood as arising from a mixture of two exponential components. The four parameters of this model are estimated via maximum‑likelihood estimation. A regionalized TCEV fitted to the 39 Italian series accurately reproduces the observed skewness and largest‑order‑statistic distributions.

Abstract

Theoretical considerations, supported by statistical analysis of 39 annual flood series (AFS) of Italian basins, suggest that the two‐component extreme value (TCEV) distribution can be assumed as a parent flood distribution, i.e., one closely representative of the real flood experience. This distribution belongs to the family of distributions of the annual maximum of a compound Poisson process, which is a solid theoretical basis for AFS analysis. However, the two‐parameter distribution of this family, obtained on the assumption of identically distributed floods, does not account for the high variability of both observed skewness and largest order statistics, so that a significant number of observed floods qualify as outliers under this distribution. The more general TCEV distribution assumes individual floods to arise from a mixture of two exponential components. Its four parameters can be estimated by the maximum likelihood method. A regionalized TCEV distribution, with parameters representative of a set of 39 Italian AFS's, was shown to closely reproduce the observed distribution of skewness and that of the largest order statistic.