Air Contaminant Statistical Distributions with Application to PM10 in Santiago, Chile

  • Carolina Marchant
  • Víctor Leiva
  • M. Fernanda Cavieres
  • Antonio Sanhueza
Part of the Reviews of Environmental Contamination and Toxicology book series (RECT, volume 223)


Breathable air is a gas mixture made up of 78 % nitrogen, 21 % oxygen, and 1 % carbon dioxide and other gases such as argon, radon, and xenon (Pani 2007). Atmospheric contamination is the presence in the air of substances that change its chemical and physical characteristics. Air pollution derives primarily from fossil fuel combustion products that are emitted into the air. In some areas, the effects of air pollution are exacerbated when climatological and geographical factors restrict its dissipation. Over the past decades, the air quality of many urban centers has seriously deteriorated. As a result, millions of people are exposed to pollution levels above the recommended limits by the World Health Organization (WHO), such as indicated by the United Nations Environment Programme. Air pollution is currently a concern in the American region, wherein several capital cities have levels that exceed national and international guideline limits. Such is the case for Santiago, the capital city of Chile, which is among the cities with higher air pollution levels in the world (Ostro 2003). The location of Santiago and the weather it experiences, when combined with high anthropological emissions, create critical air pollution conditions. The interaction of air pollution and heat can impair the health and well-being of people, particularly the elderly and children (Kinney 2008).


PM10 Concentration Extreme Value Distribution Chilean Government Extreme Value PM10 Data 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The authors wish to thank the editor, Dr. David M. Whitacre, and the referees for their constructive comments on an earlier version of this chapter, which resulted in the current version. C. Marchant gratefully acknowledges support from the scholarship “President of the Republic” of the Chilean government of which she was a recipient during her studies in engineering in statistics in the University of Valparaiso which concluded with this work. The research of V. Leiva was partially supported by FONDECYT 1120879 grant from the Chilean government. The research of A. Sanhueza was partially supported by FONDECYT 1080409.


  1. Balakrishnan N, Leiva V, Sanhueza A, Vilca F (2009) Estimation in the Birnbaum-Saunders distribution based on scale-mixture of normals and the EM-algorithm. SORT 33:171–192Google Scholar
  2. Barry PJ (1971) Use of Argon-41 to study the dispersion of stack effluents. Proc Symp Nucl Techn Environ Pollut Int. Atomic Energy Agenc 241–253Google Scholar
  3. Bencala KE, Seinfeld JH (1976) On frequency distribution of air pollutant concentrations. Atmos Environ 10:941–950CrossRefGoogle Scholar
  4. Berger A, Melice JL, Demuth CL (1982) Statistical distribution of daily and high atmospheric SO2 concentration. Atmos Environ 16:2863–2877CrossRefGoogle Scholar
  5. Birnbaum ZW, Saunders SC (1969) A new family of life distributions. J Appl Probab 6:319–327CrossRefGoogle Scholar
  6. Brauer M, Hoek G, van Vliet P, Meliefste K, Fischer P, Gehring U, Heinrich J, Cyrys J, Bellander T, Lewne M, Brunekreef B (2003) Estimating long-term average particulate air pollution concentrations, application of traffic indicators and geographic information systems. Epidemiology 14:228–239Google Scholar
  7. Brook RD, Franklin B, Cascio W, Hong Y, Howard G, Lipsett M, Luepker R, Mittleman M, Samet J, Smith SC Jr, Tager I (2004) Expert panel on population and prevention science of the American Heart Association. Air pollution and cardiovascular disease: a statement for healthcare professionals from the Expert Panel on Population and Prevention Science of the American Heart Association. Circulation 109:2655–2671CrossRefGoogle Scholar
  8. Brook RD, Rajagopalan S, Arden C, Brook JR, Bhatnagar A, Diez-Roux A, Holguin F, Hong Y, Luepker R, Mittleman MA, Peters A, Siscovick D, Smith S, Whitsel L, Kaufman J (2010) Particulate matter air pollution and cardiovascular disease: an update to the scientific statement from the American Heart Association. Circulation 121:2331–2378CrossRefGoogle Scholar
  9. Cakmak S, Dales RE, Gultekin T, Vidal CB, Farnendaz M, Rubio MA, Oyola P (2009) Components of particulate air pollution and emergency department visits in Chile. Arch Environ Occup Health 64:148–155CrossRefGoogle Scholar
  10. Cakmak S, Dales RE, Vidal CB (2010) Air pollution and hospitalization for epilepsy in Chile. Environ Int 36:501–505CrossRefGoogle Scholar
  11. CEPAL (2000) The equity gap: a second assessment. Second Regional Conference in Follow-up to the World Summit for Social Development, Santiago, ChileGoogle Scholar
  12. Cicolella A (2008) Les composes organiques volatils (COV): definition, classification et proprietes. Rev Mal Respir 25:155–163CrossRefGoogle Scholar
  13. Cifuentes L, Borja-Aburto VH, Gouveia N, Thurston G, Davis DL (2001) Assessing health benefits of urban air pollution reductions associated with climate change mitigation (2000–2020): Santiago, Sao Paulo, Mexico City, and New York City. Environ Health Perspect 109:419–425Google Scholar
  14. Cohen AJ, Anderson HR, Ostro B et al (2004) Urban air pollution. In: Ezzati M, Lopez AD, Rodgers A, Murray CJL (eds) Comparative quantification of health risks: global and regional burden of disease attributable to selected major risk factors. World Health Organization, Geneva, pp 1353–1433Google Scholar
  15. CONAMA (1998) Establece norma de calidad primaria para material particulado respirable PM10, en especial de los valores que definen situaciones de emergencia. Decreto 59 Gobierno de Chile, Santiago, ChileGoogle Scholar
  16. Curran TC, Frank NH (1975) Assessing the validity of the lognormal model when predicting maximum air pollutant concentrations. Proc 68th Ann Meet Air Pollut Control Assoc 3:51–75Google Scholar
  17. Dales RE, Cakmak S, Vidal CB (2009) Air pollution and hospitalization for headache in Chile. Am J Epidemiol 170:1057–1066CrossRefGoogle Scholar
  18. Dales RE, Cakmak S, Vidal CB (2010) Air pollution and hospitalization for venous thromboembolic disease in Chile. J Thromb Haemost 8:669–674CrossRefGoogle Scholar
  19. Deepa A, Shiva SM (2010) Statistical distribution models for urban air quality management. Int J Adv Geosci 16:285–297Google Scholar
  20. Díaz-García JA, Leiva V (2005) A new family of life distributions based on elliptically contoured distributions. J Stat Plan Inference 128:445–457, Erratum: J Stat Plan Inference 137:1512–1513CrossRefGoogle Scholar
  21. Ferreira M, Gomes MI, Leiva V (2012) On an extreme value version of the Birnbaum-Saunders distribution. RevStat Stat J 10(2):181–210Google Scholar
  22. Franco R, Sánchez-Olea R, Reyes-Reyes EM, Panayiotidis MI (2009) Environmental toxicity, oxidative stress and apoptosis: Ménage a trois. Mutat Res 674:3–22CrossRefGoogle Scholar
  23. Garreaud RD, Rutllant J (2004) Factores meteorológicos de la contaminación atmosférica en Santiago in episodios críticos de contaminación atmosférica en Santiago. R. Morales Colección de Química Ambiental, Universidad de Chile, Santiago de Chile, pp 9–36Google Scholar
  24. Gifford FA (1974) The form of the frequency distribution of air pollution concentrations. Proc Symp Statistical Aspects of Air Quality Data, EPA-650/4-74-038, pp 3.1–3.7Google Scholar
  25. Gokhale S, Khare M (2007) Statistical behavior of carbon monoxide from vehicular exhausts in urban environments. Environ Modell Softw 22:526–535CrossRefGoogle Scholar
  26. Gramsch E, Cereceda-Balic F, Oyola P, von Baer D (2006) Examination of pollution trends in Santiago de Chile with cluster analysis of PM10 and ozone data. Atmos Environ 40:5464–5475CrossRefGoogle Scholar
  27. Hedley AJ, Wong CM, Thach TQ, Ma S, Lam TH, Anderson HR (2002) Cardiorespiratory and all-cause mortality after restrictions on sulfur content of fuel in Hong Kong: an intervention study. Lancet 360:1646–1652CrossRefGoogle Scholar
  28. Hesterberg TW, Bunn WB, McClellan RO, Hamade AK, Long CM, Valberg PA (2009) Critical review of the human data on short-term nitrogen dioxide (NO2) exposures: evidence for NO2 no-effect levels. Crit Rev Toxicol 39:743–781CrossRefGoogle Scholar
  29. Holland DM, Terence FS (1982) Fitting statistical distributions to air quality data by the maximum likelihood method. Atmos Environ 16:1071–1076CrossRefGoogle Scholar
  30. Horowitz J (1980) Extreme values from a nonstationary stochastic process: an application to air quality analysis. Technometrics 22:469–478CrossRefGoogle Scholar
  31. Hubert M, Vandervieren E (2008) An adjusted boxplot for skewed distributions. Comp Stat Data Anal 52:5186–5201CrossRefGoogle Scholar
  32. Järup L (2003) Hazards of heavy metal contamination. Br Med Bull 68:167–182CrossRefGoogle Scholar
  33. Johnson NL, Kotz S, Balakrishnan N (1995) Continuous Univariate Distributions–Vol 2. Wiley, New YorkGoogle Scholar
  34. Kampa M, Castanas E (2008) Human health effects of air pollution. Environ Pollut 151:362–367CrossRefGoogle Scholar
  35. Kan H, Wong CM, Vichit-Vadakan N, Qian Z (PAPA Project Team) (2010) Short-term association between sulfur dioxide and daily mortality: the public health and air pollution in Asia (PAPA) study. Environ Res 110:258–264CrossRefGoogle Scholar
  36. Kan H, Chen B (2004) Statistical distributions of ambient air pollutants in Shanghai, China. Biomed Environ Sci 17:366–372Google Scholar
  37. Katsouyanni K (2003) Ambient air pollution and health. Br Med Bull 68:143–156CrossRefGoogle Scholar
  38. Kinney PL (2008) Climate change, air quality, and human health. Am J Prev Med 35:459–467CrossRefGoogle Scholar
  39. Larsen R (1971) A mathematical model for relating air quality measurements to air quality standards. Air Pollution Series, EPA-AP89Google Scholar
  40. Latza U, Gerdes S, Baur X (2009) Effects of nitrogen dioxide on human health: systematic review of experimental and epidemiological studies conducted between 2002 and 2006. Int J Hyg Environ Health 212:271–287CrossRefGoogle Scholar
  41. Leiva V, Barros M, Paula GA, Galea M (2007) Influence diagnostics in log-Birnbaum-Saunders regression models with censored data. Comp Stat Data Anal 51:5694–5707CrossRefGoogle Scholar
  42. Leiva V, Barros M, Paula GA, Sanhueza A (2008) Generalized Birnbaum-Saunders distributions applied to air pollutant concentration. Environmetrics 19:235–249CrossRefGoogle Scholar
  43. Leiva V, Sanhueza A, Kelmansky S, Martinez E (2009) On the glog-normal distribution and its association with the gene expression problem. Comp Stat Data Anal 53:1613–1621CrossRefGoogle Scholar
  44. Leiva V, Vilca F, Balakrishnan N, Sanhueza A (2010) A skewed sinh-normal distribution and its properties and application to air pollution. Commun Stat Theory Methods 39:426–443CrossRefGoogle Scholar
  45. Leiva V, Athayde E, Azevedo C, Marchant C (2011) Modeling wind energy flux by a Birnbaum-Saunders distribution with unknown shift parameter. J Appl Stat 38:2819–2838CrossRefGoogle Scholar
  46. Listorti JA (1999) Is environmental health really a part of economic development—or only an afterthought? Environ Urban 11:89–100CrossRefGoogle Scholar
  47. Liu G, Niu Z, Van Niekerk D, Xue J, Zheng L (2008) Polycyclic aromatic hydrocarbons (PAHs) from coal combustion: emissions, analysis, and toxicology. Rev Environ Contam Toxicol 192:1–28CrossRefGoogle Scholar
  48. Lu H-C, Fang G-C (2002) Estimating the frequency distributions of PM10 and PM2.5 by the statistics of wind speed at Sha-Lu, Taiwan. Sci Total Environ 298:119–130CrossRefGoogle Scholar
  49. Lynn DA (1974) Fitting curves to urban suspended particulate data. Statistical Aspects of Air Quality Data, EPA 650/4-74-038, pp. 13.1–13.28Google Scholar
  50. Maggiora CD, Lopez-Silva JA (2006) Vulnerability to air pollution in Latin America and the Caribbean Region. The World Bank, Latin America and the Caribbean Region, Environmentally and Socially Sustainable Development Department, Working paper No. 28Google Scholar
  51. McConnell R, Berhane K, Gilliland F, Molitor J, Thomas D, Lurmann F, Avol E, Gauderman WJ, Peters JM (2003) Prospective study of air pollution and Bronchitic symptoms in children with asthma. Am J Respir Crit Care Med 168:790–797CrossRefGoogle Scholar
  52. Morel B, Yeh S, Cifuentes L (1999) Statistical distributions for air pollution applied to the study of the particulate problem in Santiago. Atmos Environ 33:2575–2585CrossRefGoogle Scholar
  53. Muñoz F, Carvalho MS (2009) Efecto del tiempo de exposición a PM10 en las urgencias por bronquitis aguda. Cad Saude Publica 25:529–539CrossRefGoogle Scholar
  54. Nadarajah S (2008) A truncated inverted beta distribution with application to air pollution data. Stoch Environ Res Risk Assess 22:285–289CrossRefGoogle Scholar
  55. Nevers D (2000) Air Pollution Control Engineering. McGraw-Hill, New YorkGoogle Scholar
  56. Nuvolone D, Balzi D, Chini M, Scala D, Giovannini F, Barchielli A (2011) Short-term association between ambient air pollution and risk of hospitalization for acute myocardial infarction: results of the cardiovascular risk and air pollution in Tuscany (RISCAT) study. Am J Epidemiol 174:63–71CrossRefGoogle Scholar
  57. OECD-DAC (2000) Shaping the urban environment in the 21st century: from understanding to action, a DAC reference manual on urban environmental policy. Organization for Economic Cooperation and Development, ParisGoogle Scholar
  58. Ostro P (2003) Air pollution and its impacts on health in Santiago, Chile. In: McGranahan G, Murray F (eds) Air Pollution And Health In Rapidly Developing Countries. Earthscan Publications Ltd., LondonGoogle Scholar
  59. Ott WR (1990) A physical explanation of the lognormality of pollution concentrations. J Air Waste Manag Assoc 40:1378–1383CrossRefGoogle Scholar
  60. Ott WR (1995) Environmental Statistics and Data Analysis. Lewis Publishers, Boca Raton, FLGoogle Scholar
  61. Ott W, Mage D (1976) A general-purpose univariate probability model for environmental data analysis. Comput Oper Res 3:209–216CrossRefGoogle Scholar
  62. Pani B (2007) Textbook of Environmental Chemistry. Jk International Publishing House, New DelhiGoogle Scholar
  63. Pollack, R (1975) Studies of pollutant concentration frequency distributions. Environmental Monitoring Series, EPA-650/4-75-004Google Scholar
  64. Prieto C, Mancilla FP, Astudillo OP, Reyes PA, Román AO (2007) Excess respiratory diseases in children and elderly people in a community of Santiago with high particulate air pollution. Rev Med Chil 135:221–228Google Scholar
  65. Rumburg B, Alldredge R, Claiborn C (2001) Statistical distributions of particulate matter and the error associated with sampling frequency. Atmos Environ 35:2907–2920CrossRefGoogle Scholar
  66. Rutllant J, Garreaud R (1995) Meteorological air pollution potential for Santiago, Chile: towards an objective episode forecasting. Environ Monit Assess 34:223–244CrossRefGoogle Scholar
  67. Sanhueza A, Leiva V, Balakrishnan N (2008) The generalized Birnbaum-Saunders distribution and its theory, methodology and application. Commun Stat Theory Methods 37:645–670CrossRefGoogle Scholar
  68. Satterthwaite D (1997) Sustainable cities or cities that contribute to sustainable development. Urban Studies 34:1667–1691CrossRefGoogle Scholar
  69. Schecter A, Birnbaum LS, Ryan J, Constable J (2006) Dioxins: an overview. Environ Res 101:419–428CrossRefGoogle Scholar
  70. Scriven RA (1971) Use of Argon-41 to study the dispersion of stack effluents. Proc Symp Nucl Techn Environ Pollut 253-255Google Scholar
  71. Sedek JNM, Ramli NA, Yahaya AS (2006) Air quality predictions using lognormal distribution functions of particulate matter in Kuala Lumpur Malaysia. J Environ Manag 7:33–41Google Scholar
  72. Simpson RW, Butt J, Jakeman AJ (1984) An averaging time model of SO2 frequency distributions from a single point source. Atmos Environ 18:1115–1123CrossRefGoogle Scholar
  73. Singpurwalla N (1972) Extreme values from a lognormal law with applications to air pollution problems. Technometrics 14:703–711CrossRefGoogle Scholar
  74. Soliman ASM, Palmer GM, Jacko RB (2006) Development of an empirical model to estimate real world fine particulate matter emission factors, the traffic air quality model. J Air Waste Manag Assoc 56:1540–1549CrossRefGoogle Scholar
  75. Taylor RA, Jakeman AJ, Simpson RW (1986) Modeling distributions of air pollutant concentrations. Identification of statistical models. Atmos Environ 20:1781–1789CrossRefGoogle Scholar
  76. Tsukatani T, Shigemitsu K (1980) Simplified Pearson distributions applied to air pollutant concentration. Atmos Environ 14:245–253CrossRefGoogle Scholar
  77. Tukey JW (1977) Exploratory Data Analysis. Addison-Wesley, Reading, MAGoogle Scholar
  78. van Roosbroeck S, Wichmann J, Janssen NA, Hoek G, van Wijnen JH, Lebret E, Brunekreef B (2006) Long-term personal exposure to traffic-related air pollution among school children, a validation study. Sci Total Environ 368:565–573CrossRefGoogle Scholar
  79. Vilca F, Leiva V (2006) A new fatigue life model based on the family of skew elliptic distributions. Commun Stat Theory Methods 35:229–244CrossRefGoogle Scholar
  80. Vilca F, Sanhueza A, Leiva V, Christakos G (2010) An extended Birnbaum-Saunders model and its application in the study of environmental quality in Santiago, Chile. Stoch Environ Res Risk Assess 24:771–782CrossRefGoogle Scholar
  81. Vilca F, Santana L, Leiva V, Balakrishnan N (2011) Estimation of extreme percentiles in Birnbaum-Saunders distributions. Comp Stat Data Anal 55:1665–1678CrossRefGoogle Scholar
  82. White SS, Birnbaum LS (2009) An overview of the effects of dioxins and dioxin-like compounds on vertebrates, as documented in human and ecological epidemiology. J Environ Sci Health C 27:197–211Google Scholar
  83. WHO –World Health Organization– (2005) Air quality management global update particulate matter, ozone, nitrogen oxide and sulfur dioxide. Reg Off Europe, CopenhagenGoogle Scholar
  84. World Bank (2001) World development report 200012001, attacking poverty. Oxford University Press, OxfordGoogle Scholar

Copyright information

© Springer New York 2013

Authors and Affiliations

  • Carolina Marchant
    • 1
  • Víctor Leiva
    • 1
  • M. Fernanda Cavieres
    • 2
  • Antonio Sanhueza
    • 3
  1. 1.Departamento de EstadísticaUniversidad de ValparaísoValparaísoChile
  2. 2.Facultad de FarmaciaUniversidad de ValparaísoValparaísoChile
  3. 3.Departamento de Matemática y EstadísticaUniversidad de La FronteraTemucoChile

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