Title: An improved prior choice for Gumbel distribution parameters to model extreme values
Authors: M Isabel Parra Arevalo - Universidad de Extremadura (Spain) [presenting]
Eva Lopez Sanjuan - Universidad de Extremadura (Spain)
Mario Martinez Pizarro - University of Extremadura (Spain)
Francisco Javier Acero Diaz - University of Extremadura (Spain)
Abstract: The Gumbel distribution can be employed to model the maximum (or the minimum) of a sequence of observations. Bayesian estimation (block maxima method) for its two parameters is usually performed by using only record values of the observations, consequently a lot of information is wasted. The proposed method seizes all the available observations in order to increase the accuracy of the estimations. The key is to consider the existing relationship between the parameters of the baseline distribution for the observations and the ones for the extreme Gumbel distribution. To evaluate the performance of the proposed method, replicated data sets from different baseline distributions in the Gumbel domain of attraction are simulated. Overall, the results show that the proposed method outperforms block maxima method for the estimation of both parameters.