Title: An improved prior choice for Gumbel distribution parameters
Authors: Francisco Javier Acero Diaz - University of Extremadura (Spain)
Ruben Gomez Gonzalez - Universidad de Extremadura (Spain)
Jacinto Martin Jimenez - Universidad de Extremadura (Spain)
M Isabel Parra Arevalo - Universidad de Extremadura (Spain) [presenting]
Abstract: The methods for parameter estimation of the extreme-value distributions use only a few observations. When the focus is on modeling the extreme data based on block maxima approach using Gumbel distribution, only one observation from each block is used. A strategy that allows us to take advantage of the information from all available observations is proposed, pursuing the objective of increasing the accuracy of Bayesian parameters estimation. It consists on harnessing the existing relationship between the parameters of baseline and Gumbel distributions to obtain informative prior distributions. Our method shows good performance when dealing with very shortened available data. Different statistical analysis tests are used to compare the performance and the standard algorithm. The empirical effectiveness of the approach is demonstrated through a simulation study and a case study. Reduction in the credible interval width and enhancement in parameter location show that approach based on highly informative prior adapt to very shortened data better than the standard method does.