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

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Abstract

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.

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References

  1. Achcar, J.A., Fernández-Bremauntz, A.A., Rodrigues, E.R., Tzintzun, G. (2008). Estimating the number of ozone peaks in Mexico City using a non-homogeneous Poisson model. Environmetrics, 19, 469–485.

    Article  CAS  Google Scholar 

  2. Achcar, J.A., Rodrigues, E.R., Paulino, C.D., Soares, P. (2010). Non-homogeneous Poisson models with a change-point: an application to ozone peaks in Mexico City. Environmental and Ecological Statistics, 17, 521–541. doi:10.1007/s10651-009-01114-3.

    Article  CAS  Google Scholar 

  3. Achcar, J.A., Rodrigues, E.R., Tzintzun, G. (2011). Using non-homogeneous Poisson models with multiple change-points to estimate the number of ozone exceedances in Mexico City. Environmetrics, 22, 1–12. doi:10.002/env.1029.

    Article  CAS  Google Scholar 

  4. Achcar, J.A., Rodrigues, E.R., Tzintzun, G. (2011). Modelling interoccurrence time between ozone peaks in Mexico City in the presence of multiple change-points. Brazilian Journal of Probability and Statistics, 25, 183–204.

    Article  Google Scholar 

  5. Achcar, J.A., Rodrigues, E.R., Tarumoto, M.H. (2011). Using counting processes to estimate the number of ozone exceedances: an application to the Mexico City measurements. In Proceedings of the 58th ISI world statistics congress, Dublin, 21–16 August 2011. http://isi2011.congressplanner.eu/CPS58-04.

  6. Álvarez, L.J., Fernández-Bremauntz, A.A., Rodrigues, E.R., Tzintzun, G. (2005). Maximum a posteriori estimation of the daily ozone peaks in Mexico City. Journal of Agricultural, Biological, and Environmental Statistics, 10, 276–290.

    Article  Google Scholar 

  7. Austin, J., & Tran, H. (1999). A characterization of the weekday-weekend behavior of ambient ozone concentrations in California. In Air pollution VII (pp. 645–661). USA: WIT Press.

    Google Scholar 

  8. Bell, M.L, McDermontt, A., Zeger, S.L., Samet, J.M., Dominici, F. (2004). Ozone and short-term mortality in 95 US urban communities, 1987–2000. Journal of the American Medical Society, 292, 2372–2378. doi:10.1001/jama.292.19.2372.

    CAS  Google Scholar 

  9. Bell, M.L., Peng, R., Dominici, F. (2005). The exposure-response curve for ozone and risk of mortality and the adequacy of current ozone regulations. Environmental Health Perspectives, 114, 532–536.

    Article  Google Scholar 

  10. Bell, M.L., Goldberg, R., Rogrefe, C., Kinney, P.L., Knowlton, K., Lynn, B., Rosenthal, J., Rosenzweig, C., Patz, J.A. (2007). Climate change, ambient ozone, and health in 50 US cities. Climate Change, 82, 61–76.

    Article  CAS  Google Scholar 

  11. Davis, L.W. (2008). The effect of driving restrictions on air quality in Mexico City. Journal of Political Economy, 116, 39–81.

    Google Scholar 

  12. Flaum, J.B., Rao, S.T., Zurbenko, I.G. (1996). Moderating influence of meteorological conditions on ambient ozone concentrations. Journal of Air and Waste Management Association, 46, 33–46.

    Article  Google Scholar 

  13. Gauderman, W.J., Avol, E., Gililand, F., Vora, H., Thomas, D., Berhane, K., McConnel, R., Kuenzli, N., Lurmman, F., Rappaport, E. (2004). The effects of air pollution on lung development from 10 to 18 years of age. The New England Journal of Medicine, 351, 1057–1067.

    Article  CAS  Google Scholar 

  14. Horowitz, J. (1980). Extreme values from a nonstationary stochastic process: an application to air quality analysis. Technometrics, 22, 469–482.

    Article  Google Scholar 

  15. Huerta, G., & Sansó, B. (2007). Time-varying models for extreme values. Environmental and Ecological Statistics, 14, 285–299. doi:10.1007/s10651-007-0014-3.

    Article  CAS  Google Scholar 

  16. Javits, J.S. (1980). Statistical interdependencies in the ozone national ambient air quality standard. Journal of Air Pollution Control Association, 30, 58–59.

    Article  Google Scholar 

  17. Lanfredi, M., & Macchiato, M. (1997). Searching for low dimensionality in air pollution time series. Europhysics Letter, 40, 589–594.

    Article  CAS  Google Scholar 

  18. Leadbetter, M.R. (1991). On a basis for “peak over threshold” modeling. Statistics and Probability Letters, 12, 357–362.

    Article  Google Scholar 

  19. Lippmann, M., & Schlesinger, R.B. (2000). Toxicological bases for the setting of health-related air pollution standard. Annual Review Public Health, 21, 309–333.

    Article  CAS  Google Scholar 

  20. Loomis, D., Borja-Arbuto, V.H., Bangdiwala, S.I., Shy, C.M. (1996). Ozone exposure and daily mortality in Mexico City: a time series analysis. Health Effects Institute Research Report, 75, 1–46.

    Google Scholar 

  21. McKinley, G., Zuk, M., Höjer, M., Avalos, M., Gonzaléz, I., Iniestra, R., Laguna, I., Martínez, M.A., Osnaya, P., Reynales, L.M., Valdés, R., Martínez, J. (2005). Quantification of local and global benefits from air pollution control in Mexico City. Environmental Science Technology, 39, 1954–1961.

    Article  CAS  Google Scholar 

  22. NOM (2002). Modificación a la Norma Oficial Mexicana NOM-020-SSA1-1993. Diario Oficial de la Federación, 30 de Octubre de 2002 (in Spanish)

  23. O’Neill, M.R., Loomis, D., Borja-Aburto, V.H. (2004). Ozone, area social conditions and mortality in Mexico City. Environmental Research, 94, 234–242.

    Article  Google Scholar 

  24. Pan, J.N., & Chen, S.T. (2008). Monitoring long-memory air quality data using ARFIMA model. Environmetrics, 19, 209–219.

    Article  CAS  Google Scholar 

  25. Raftery, A.E. (1989). Are ozone exceedance rate decreasing? Comment of the paper “Extreme value analysis of environmental time series: an application to trend detection in ground-level ozone” by R.L. Smith. Statistical Sciences, 4, 378–381.

    Article  Google Scholar 

  26. Roberts, E.M. (1979). Review of statistics of extreme values with applications to air quality data. Part I. Review. Journal of the Air Pollution Control Association, 29, 632–637.

    Article  Google Scholar 

  27. Roberts, E.M. (1979). Review of statistics of extreme values with applications to air quality data. Part II. Applications. Journal of the Air Pollution Control Association, 29, 733–740.

    Article  CAS  Google Scholar 

  28. Smith, R.L. (1989). Extreme value analysis of environmental time series: an application to trend detection in ground-level ozone. Statistical Sciences, 4, 367–393.

    Article  Google Scholar 

  29. Spiegelhalter, D.J., Thomas, A., Best, N.G., Gilks, W.R. (1999). WinBugs: Bayesian inference using gibbs sampling. Cambridge: MRC Biostatistics Unit.

    Google Scholar 

  30. Spiegelhalter, D.J., Best, N.G., Carlin, B.P., Van der Linde, A. (2002). Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society Series B, 64, 583–639.

    Article  Google Scholar 

  31. Zavala, M., Herndon, S.C., Wood, E.C., Onasch, T.B., Knighton, W.B., Marr, L.C., Kolb, C.E., Molina, L.T. (2009). Evaluation of mobile emissions contributions to Mexico City’s emissions inventory using on road and cross-road emission measurements and ambient data. Atmospheric Chemistry and Physics, 9, 6305–6317.

    Article  CAS  Google Scholar 

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Acknowledgements

We thank an anonymous reviewer and the editor in chief for the constructive comments and suggestions that helped to improve the presentation of this work. The authors thank Guadalupe Tzintzun from the Instituto Nacional de Ecología of the Secretaría de Medio Ambiente y Recursos Naturales, Mexico, for providing the ozone data. ERR received financial support from the project PAPIIT-IN104110-3 of the Dirección General de Apoyo al Personal Académico of the Universidad Nacional Autónoma de México, Mexico. JAA was partially supported by the grant number 300235/2005-4 of the Conselho Nacional de Pesquisa, Brazil.

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Authors and Affiliations

  1. Departamento de Medicina Social, Faculdade de Medicina de Ribeirão Preto, USP, Av. Bandeirantes, 3900, 14049-900, Ribeirão Preto, São Paulo, Brazil

    Jorge A. Achcar

  2. Instituto de Matemáticas, Universidad Nacional Autónoma de México, Circuito Exterior – Ciudad Universitaria, Mexico City, 04510, Mexico

    Eliane R. Rodrigues

  3. Departamento de Estadística, Universidad Nacional de Colombia, Bogotá, Colombia

    Edilberto Cepeda-Cuervo

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  1. Jorge A. Achcar
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  2. Eliane R. Rodrigues
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  3. Edilberto Cepeda-Cuervo
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Correspondence to Eliane R. Rodrigues.

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Achcar, J.A., Rodrigues, E.R. & Cepeda-Cuervo, E. Some Dependence Models for the Time Between Ozone Exceedances in Mexico City. Environ Model Assess 18, 259–270 (2013). https://doi.org/10.1007/s10666-012-9347-x

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