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.
Highlights
Inhabitants of large cities throughout the world may present health problems related to high levels of pollution
We would like to know how emergency alert situations would be if 0.17 ppm, instead of 0.2 ppm, was the threshold considered to declare them in Mexico City
One of the aims here is to compare the fit of different rate functions, considered in the literature, to the ozone data from Mexico City obtained after a series of environmental measures were taken to decrease air pollution levels
Summary
Inhabitants of large cities throughout the world may present health problems related to high levels of pollution. One of the aims here is to compare the fit of different rate functions, considered in the literature, to the ozone data from Mexico City obtained after a series of environmental measures were taken to decrease air pollution levels. When the best Poisson model is selected for the data considered here, we may perform inference about the mean time between surpassings of the 0.17 ppm threshold and about the probability of a certain number of exceedances in a time interval of interest Another aim here is to present the code in R when some of the functions are used so the readers can use them in their own studies if the situation arises. Some of the computer programmes used in the estimation of the parameters can be obtained from https://sites.google.com/site/jmbarrios/recursos/result-rep orts-for-jep
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