Open Access Open Access  Restricted Access Subscription or Fee Access

Estimation of extreme quantiles for non stationary Gumbel models in the case of non linear normalization

G. C. Okou, K. K. Keita, A. Kamagaté


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).


extreme value theory, non-stationary, non linear normalization, Quasi-Newton Algorithm, BSM method, extreme quantiles.

Full Text:


Disclaimer/Regarding indexing issue:

We have provided the online access of all issues and papers to the indexing agencies (as given on journal web site). It’s depend on indexing agencies when, how and what manner they can index or not. Hence, we like to inform that on the basis of earlier indexing, we can’t predict the today or future indexing policy of third party (i.e. indexing agencies) as they have right to discontinue any journal at any time without prior information to the journal. So, please neither sends any question nor expects any answer from us on the behalf of third party i.e. indexing agencies.Hence, we will not issue any certificate or letter for indexing issue. Our role is just to provide the online access to them. So we do properly this and one can visit indexing agencies website to get the authentic information. Also: DOI is paid service which provided by a third party. We never mentioned that we go for this for our any journal. However, journal have no objection if author go directly for this paid DOI service.