This paper deals with the use of the Dagum distribution to model the maximum daily levels of tropospheric ozone. We compare the fit of the Dagum distribution against the Generalized Extreme Value distribution (GEV) by using the Kolmogorov-Smirnov test and the Akaike criterion for model selection. Also we propose a methodology for estimating long term trends in the daily maxima of tropospheric ozone by using the Vector Generalized Linear Model (VGLM) and quantiles of the Dagum distribution. Ozone data from Pedregal Station in Mexico City (one with the worst air pollution in the World) are analyzed for the period 2001-2008. Results show that the Dagum model has a similar or better fit than the GEV model. The quantiles of Dagum distribution and VGLM show evidence of a downward trend in high ozone levels at Pedregal Station.