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Predicting PM2.5 and PM10 Levels during Critical Episodes Management in Santiago, Chile, with a Bivariate Birnbaum-Saunders Log-Linear Model

Author

Listed:
  • Rodrigo Puentes

    (National Medical Devices, Innovation and Development Agency, Instituto de Salud Pública de Chile, Santiago 7780050, Chile)

  • Carolina Marchant

    (Faculty of Basic Sciences, Universidad Católica del Maule, Talca 3480112, Chile
    ANID-Millennium Science Initiative Program-Millennium Nucleus Center for the Discovery of Structures in Complex Data, Santiago 7820244, Chile)

  • Víctor Leiva

    (School of Industrial Engineering, Pontificia Universidad Católica de Valparaíso, Valparaíso 2362807, Chile)

  • Jorge I. Figueroa-Zúñiga

    (Department of Statistics, Universidad de Concepción, Concepción 4070386, Chile)

  • Fabrizio Ruggeri

    (Consiglio Nazionale delle Ricerche, Istituto di Matematica Applicata e Tecnologie Informatiche, 20133 Milano, Italy)

Abstract

Improving air quality is an important environmental challenge of our time. Chile currently has one of the most stable and emerging economies in Latin America, where human impact on natural resources and air quality does not go unperceived. Santiago, the capital of Chile, is one of the cities in which particulate matter (PM) levels exceed national and international limits. Its location and climate cause critical conditions for human health when interaction with anthropogenic emissions is present. In this paper, we propose a predictive model based on bivariate regression to estimate PM levels, related to PM2.5 and PM10, simultaneously. Birnbaum-Saunders distributions are used in the joint modeling of real-world PM2.5 and PM10 data by considering as covariates some relevant meteorological variables employed in similar studies. The Mahalanobis distance is utilized to assess bivariate outliers and to detect suitability of the distributional assumption. In addition, we use the local influence technique for analyzing the impact of a perturbation on the overall estimation of model parameters. In the predictions, we check the categorization for the observed and predicted cases of the model according to the primary air quality regulations for PM.

Suggested Citation

  • Rodrigo Puentes & Carolina Marchant & Víctor Leiva & Jorge I. Figueroa-Zúñiga & Fabrizio Ruggeri, 2021. "Predicting PM2.5 and PM10 Levels during Critical Episodes Management in Santiago, Chile, with a Bivariate Birnbaum-Saunders Log-Linear Model," Mathematics, MDPI, vol. 9(6), pages 1-24, March.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:6:p:645-:d:519378
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    References listed on IDEAS

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    1. Víctor Leiva & Helton Saulo & Rubens Souza & Robert G. Aykroyd & Roberto Vila, 2021. "A new BISARMA time series model for forecasting mortality using weather and particulate matter data," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 40(2), pages 346-364, March.
    2. Francisco J. A. Cysneiros & Víctor Leiva & Shuangzhe Liu & Carolina Marchant & Paulo Scalco, 2019. "A Cobb–Douglas type model with stochastic restrictions: formulation, local influence diagnostics and data analytics in economics," Quality & Quantity: International Journal of Methodology, Springer, vol. 53(4), pages 1693-1719, July.
    3. Victor Leiva & Carolina Marchant & Fabrizio Ruggeri & Helton Saulo, 2015. "A criterion for environmental assessment using Birnbaum–Saunders attribute control charts," Environmetrics, John Wiley & Sons, Ltd., vol. 26(7), pages 463-476, November.
    4. J. Marcus Jobe & Michael Pokojovy, 2015. "A Cluster-Based Outlier Detection Scheme for Multivariate Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(512), pages 1543-1551, December.
    5. Agulló, Jose & Croux, Christophe & Van Aelst, Stefan, 2008. "The multivariate least-trimmed squares estimator," Journal of Multivariate Analysis, Elsevier, vol. 99(3), pages 311-338, March.
    6. Kwangil Ro & Changliang Zou & Zhaojun Wang & Guosheng Yin, 2015. "Outlier detection for high-dimensional data," Biometrika, Biometrika Trust, vol. 102(3), pages 589-599.
    7. Carolina Marchant & Víctor Leiva & Francisco José A. Cysneiros & Juan F. Vivanco, 2016. "Diagnostics in multivariate generalized Birnbaum-Saunders regression models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(15), pages 2829-2849, November.
    8. Luis Sánchez & Víctor Leiva & Manuel Galea & Helton Saulo, 2021. "Birnbaum‐Saunders quantile regression and its diagnostics with application to economic data," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 37(1), pages 53-73, January.
    9. Kundu, Debasis & Balakrishnan, N. & Jamalizadeh, A., 2010. "Bivariate Birnbaum-Saunders distribution and associated inference," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 113-125, January.
    10. Ramón Giraldo & Luis Herrera & Víctor Leiva, 2020. "Cokriging Prediction Using as Secondary Variable a Functional Random Field with Application in Environmental Pollution," Mathematics, MDPI, vol. 8(8), pages 1-13, August.
    11. Robert G. Aykroyd & Víctor Leiva & Carolina Marchant, 2018. "Multivariate Birnbaum-Saunders Distributions: Modelling and Applications," Risks, MDPI, vol. 6(1), pages 1-25, March.
    12. Suelena S. Rocha & Patrícia L. Espinheira & Francisco Cribari‐Neto, 2021. "Residual and local influence analyses for unit gamma regressions," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 75(2), pages 137-160, May.
    13. Carolina Marchant & Víctor Leiva & George Christakos & M. Fernanda Cavieres, 2019. "Monitoring urban environmental pollution by bivariate control charts: New methodology and case study in Santiago, Chile," Environmetrics, John Wiley & Sons, Ltd., vol. 30(5), August.
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    Cited by:

    1. Nicole Jeldes & Germán Ibacache-Pulgar & Carolina Marchant & Javier Linkolk López-Gonzales, 2022. "Modeling Air Pollution Using Partially Varying Coefficient Models with Heavy Tails," Mathematics, MDPI, vol. 10(19), pages 1-24, October.
    2. Yousif Alyousifi & Kamarulzaman Ibrahim & Mahmod Othamn & Wan Zawiah Wan Zin & Nicolas Vergne & Abdullah Al-Yaari, 2022. "Bayesian Information Criterion for Fitting the Optimum Order of Markov Chain Models: Methodology and Application to Air Pollution Data," Mathematics, MDPI, vol. 10(13), pages 1-16, June.
    3. Xiangxue Zhang & Yue Lin & Changxiu Cheng & Junming Li, 2021. "Determinant Powers of Socioeconomic Factors and Their Interactive Impacts on Particulate Matter Pollution in North China," IJERPH, MDPI, vol. 18(12), pages 1-15, June.

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