Weibull and generalised exponential overdispersion models with an application to ozone air pollution

We consider the problem of estimating the mean and variance of the time between occurrences of an event of interest (inter-occurrences times) where some forms of dependence between two consecutive time intervals are allowed. Two basic density functions are taken into account. They are the Weibull and the generalised exponential density functions. In order to capture the dependence between two consecutive inter-occurrences times, we assume that either the shape and/or the scale parameters of the two density functions are given by auto-regressive models. The expressions for the mean and variance of the inter-occurrences times are presented. The models are applied to the ozone data from two regions of Mexico City. The estimation of the parameters is performed using a Bayesian point of view via Markov chain Monte Carlo (MCMC) methods.

Conselho Nacional de Pesquisa (Brazil)

Conselho Nacional de Pesquisa, Brazil [300235/2005-4]

Direccion General de Apoyo al Personal Academico de la Universidad Nacional Autonoma de Mexico [PAPIIT-IN104110-3]

Direccion General de Apoyo al Personal Academico de la Universidad Nacional Autonoma de Mexico

Department of Statistics of the Universidad Nacional de Colombia

Department of Statistics of the Universidad Nacional de Colombia

Instituto de Ciencias Matematicas e de Computacao of the Universidade of Sao Paulo-Sao Carlos, Brazil

Instituto de Ciencias Matematicas e de Computacao of the Universidade of Sao PauloSao Carlos, Brazil