A0297
Title: An extended generalized Pareto regression model for count data
Authors: Touqeer Ahmad - ENSAI (France) [presenting]
Carlo Gaetan - Ca' Foscari University of Venice (Italy)
Philippe Naveau - CNRS-IPSL (France)
Abstract: The statistical modeling of discrete extremes has received less attention than its continuous counterparts in the extreme value theory literature. One approach to the transition from continuous to discrete extremes is the modeling of threshold exceedances of integer random variables by the discrete version of the generalized Pareto distribution. However, the optimal choice of thresholds defining exceedances remains a problematic issue. Moreover, in a regression framework, the treatment of the majority of non-extreme data below the selected threshold is either ignored or separated from the extremes. To tackle these issues, the concept of employing a smooth transition between the bulk and the upper tail of the distribution is expanded on. In the case of zero inflation, models are also developed with an additional parameter. To incorporate possible predictors, the parameters are related to additive smoothed predictors via an appropriate link, as in the generalized additive model framework. A penalized maximum likelihood estimation procedure is implemented. The modeling proposal is illustrated with a real dataset of avalanche activity in the French Alps. With the advantage of bypassing the threshold selection step, the results indicate that the proposed models are more flexible and robust than competing models, such as the negative binomial distribution.
