Some Dependence Models for the Time Between Ozone Exceedances in Mexico City

In this paper, we consider several modelling approaches for the mean time between exceedances of a given environmental threshold. The interest here resides in the time between ozone exceedances (also called ozone inter-exceedances times). The proposed models assume two basic density functions for the time between surpassings: the Weibull and the generalised exponential functions. Considering those distributions, a random effect with autoregressive structure is taken into account to determine unexpected changes in the mean of the inter-exceedances density functions. Those unexpected changes could be captured either by their scale parameter or by both their scale and shape parameters. The models are applied to ozone data from the monitoring network of Mexico City. Selection of the model that best explains the data is performed using the deviance information criterion and also the sum of the absolute values of the differences between the estimated and observed means of the inter-exceedances times. An analysis to detect the possible presence of change-points is also presented.