Comparing the Adequacy of Some Non-Homogeneous Poisson Models to Estimate Ozone Exceedances in Mexico City

Jorge A. Achcar, Juan M. Barrios, Eliane R. Rodrigues

Faculdade de Medicina de Ribeir?o Preto, Universidade de S?o Paulo, S?o Paulo, Brazil.
Facultad de Ciencias, Universidad Nacional Autónoma de México, Mexico City, Mexico.
Instituto de Matemáticas, Universidad Nacional Autónoma de México, Mexico City, Mexico.

DOI: 10.4236/jep.2012.329139                

Abstract

We consider some non-homogeneous Poisson models to estimate the mean number of times that a given environmental threshold of interest is surpassed by a given pollutant. Seven different rate functions for the Poisson processes describing the models are taken into account. The rate functions considered are the Weibull, exponentiated-Weibull, and their generalisation the Beta-Weibull rate function. We also use the Musa-Okumoto, the Goel-Okumoto, a generalised Goel- Okumoto and the Weibull-geometric rate functions. Whenever thought justifiable, the model allowing the presence of change-points is also going to be considered. The different models are applied to the daily maximum ozone measurements data provided by the monitoring network of the Metropolitan Area of Mexico City. The aim is to compare the adjustment of different rate functions to the data. Even though, some of the rate functions have been considered before, now we are applying them to the same data set. In previous works they were used in different data sets and therefore a comparison of the adequacy of those models were not possible. The measurements considered here were obtained after a series of environmental measures were implemented in Mexico City. Hence, the data present a different behaviour from that of earlier studies.

Keywords

MCMC Algorithms; Non-Homogeneous Poisson Models; Change-Points; Ozone Air Pollution; Mexico City

Conflicts of Interest

The authors declare no conflicts of interest.

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