Abstract
The stationarity hypothesis is essential in hydrological frequency analysis and statistical inference. This assumption is often not fulfilled for large observed datasets, especially in the case of hydro-climatic variables. The Generalized Extreme Value distribution with covariates allows to model data in the presence of non-stationarity and/or dependence on covariates. Linear and non-linear dependence structures have been proposed with the corresponding fitting approach. The objective of the present study is to develop the GEV model with B-Spline in a Bayesian framework. A Markov Chain Monte Carlo (MCMC) algorithm has been developed to estimate quantiles and their posterior distributions. The methods are tested and illustrated using simulated data and applied to meteorological data. Results indicate the better performance of the proposed Bayesian method for rainfall quantile estimation according to BIAS and RMSE criteria especially for high return period events.
Highlights
Many fields of modern science and engineering have to deal with rare events with significant consequences
The main objective of the present study is to develop the Generalized Extreme Value model with covariates where the dependence structure is represented by B-spline functions in a Bayesian framework
We present the Generalized Extreme Value (GEV) model with covariates where the dependence structure is given by B-Splines
Summary
Many fields of modern science and engineering have to deal with rare events with significant consequences. Extreme value theory (EVT) allows to providing the basis for the statistical modeling of such extremes. The main result of EVT shows that the maxima, of Independent and Identically Distributed (i.i.d.) events, are asymptotically Generalized Extreme Value (GEV) distributed [1]. The hypotheses of the EVT are, generally, not fulfilled, and a classical frequency analysis, of independent, homogeneous and stationary samples, is considered with a large range of probability distributions to estimate the occurrence of extreme events. The Stationarity assumption is essential to carry out a statistical frequency analysis. In many fields, such as hydroclimatology, observed data series are not stationary [6,7]. Two main types of non-stationarity have been observed due to temporal trends or cycles corresponding to the effect of other co-
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