Extreme limit distribution of truncated models for daily rainfall

Abstract

AbstractWe propose truncated and power‐transformed (TPT) models for daily rainfall and we derive the generalized extreme value (GEV) limit distributions for these models. We find that these limit distributions belong to the domain of attraction of the Fréchet family when the parent distribution of the daily values is a TPT t‐Student model. In this case, the shape parameter of the limiting GEV model depends on the degrees of freedom and the power transformation parameter. When the parent distribution of the daily values is a TPT Normal model, the limiting GEV model is independent of the parameters of the parent model. We perform a detailed inference and predictive analysis to verify these theoretical results using a Bayesian approach. Markov Chain Monte Carlo methods (MCMC) were used to estimate the posterior distribution of the parameters of the t‐Student model for daily rainfall on one hand, and to estimate the posterior distribution of the parameters of the GEV model for the annual maxima on the other hand. Numerical results are presented for two locations: Maiquetía (Vargas State), and La Mariposa (Miranda State), Venezuela. Simulations from the predictive distribution of the daily values suggest a good approximation between the extreme distribution of the TPT t‐Student model and the Fréchet model found by standard extreme value limit theory. Copyright © 2009 John Wiley & Sons, Ltd.