Vazquez-Morales, Juan A. and Rodrigues, Eliane R. and Reyes-Cervantes, Hortensia J. (2024) Bivariate Analysis of Pollutants Monthly Maxima in Mexico City Using Extreme Value Distributions and Copula. Journal of Environmental Protection, 15 (07). pp. 796-826. ISSN 2152-2197
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Abstract
In the present work, we are interested in studying the joint distributions of pairs of the monthly maxima of the pollutants used by the environmental authorities in Mexico City to classify the air quality in the metropolitan area. In order to obtain the joint distributions a copula will be considered. Since we are analyzing the monthly maxima, the extreme value distributions of Weibull and Fréchet are taken into account. Using these two distributions as marginal distributions in the copula a Bayesian inference was made in order to estimate the parameters of both distributions and also the association parameters appearing in the copula model. The pollutants taken into account are ozone, nitrogen dioxide, sulphur dioxide, carbon monoxide, and particulate matter with diameters smaller than 10 and 2.5 microns obtained from the Mexico City monitoring network. The estimation was performed by taking samples of the parameters generated through a Markov chain Monte Carlo algorithm implemented using the software OpenBugs. Once the algorithm is implemented it is applied to the pairs of pollutants where one of the coordinates of the pair is ozone and the other varies on the set of the remaining pollutants. Depending on the pollutant and the region where they were collected, different results were obtained. Hence, in some cases we have that the best model is that where we have a Fréchet distribution as the marginal distribution for the measurements of both pollutants and in others the most suitable model is the one assuming a Fréchet for ozone and a Weibull for the other pollutant. Results show that, in the present case, the estimated association parameter is a good representation to the correlation parameters between the pair of pollutants analyzed. Additionally, it is a straightforward task to obtain these correlation parameters from the corresponding association parameters.
Item Type: | Article |
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Subjects: | Academic Digital Library > Agricultural and Food Science |
Depositing User: | Unnamed user with email info@academicdigitallibrary.org |
Date Deposited: | 24 Jul 2024 12:16 |
Last Modified: | 24 Jul 2024 12:16 |
URI: | http://publications.article4sub.com/id/eprint/3388 |