Estimation of extreme quantiles for non stationary Gumbel models in the case of non linear normalization
The extreme value theory is frequently used to analyze flood flows in hydrology. Originally, this theory was developed for independent and identically distributed observations (iid). Gumbel models are among the most commonly used probability functions in frequency analysis of extreme flood flows. In practice, iid condition is not always verified. In this paper, we estimate extreme quantiles using non-stationary Gumbel models in the case of non linear normalization (power normalization). The parameters of these models are estimated from numerical methods such as Maximum Likelihood/Quasi-Newton Algorithm (MLE/QN) and Block Subdivision Method (BSM). We test non-stationary Gumbel models in a case study using station water level data. These data are observed over time (t).
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