Title: Parameter estimation of the generalized Pareto distribution for normal baseline distribution
Authors: Eva Lopez Sanjuan - Universidad de Extremadura (Spain) [presenting]
M Isabel Parra Arevalo - Universidad de Extremadura (Spain)
Jacinto Martin Jimenez - Universidad de Extremadura (Spain)
Mario Martinez Pizarro - University of Extremadura (Spain)
Abstract: In Extreme Value Theory, the estimation of the limit distribution is usually made discarding an important amount of data. When we apply peaks-over-threshold method, for Generalized Pareto Distribution (GPD), only values above a certain threshold are considered and much information is wasted. We employ all the available data to make estimations for the parameters of the GPD, taking advantage of the existing relationship between the parameters of baseline distribution and the limit ones. We focus on the case when the baseline distribution is Normal. Different simulations were carried out in order to compare the effectiveness of this strategy to the standard Metropolis-Hastings algorithm. Besides, the accuracy of the method is tested employing real data, provided by Red Automatica de Monitoreo Atmosferico (RAMA), corresponding to the levels of PM2.5, the most dangerous polluting agent in Ciudad de Mexico between 2003 and 2019.