Use of the Three-parameter Burr XII Distribution for Modelling Ambient Daily Maximum Nitrogen Dioxide Concentrations in the Gaborone Fire Brigade
Keywords:
pollution, nitrogen dioxide, Burr Type XII, Dagum, log-logistic, maximum likelihood estimate.Abstract
Air pollution constitutes one of the major problems in urban areas where many sources of airborne pollutants are concentrated. Identifying an appropriate probability model to describe the stochastic behaviour of extreme ambient air pollution level for a specific site or multiple sites forms an integral part of environmental management and pollution control. This paper proposes the use of the three-parameter Burr Type XII distribution to model maximum levels of nitrogen dioxide at a specific site. The study focuses on the daily maximum ambient nitrogen dioxide concentrations for Gaborone Fire Brigade in the winter season, May-July, 2014. The fit of the three-parameter Burr Type XII is compared to that of the three-parameter Dagum and three-parameter log-logistic by using the Kolmogorov-Smirnov and Anderson-Darling criterion for model selection. It is found that the three-parameter Burr Type XII gives the best fit, followed by the log-logistic and the Dagum I, in that order. The results justify the use of the three-parameter Burr Type XII to model ambient air pollution extreme values.
References
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[2] L. Curtis, W. Rea, P. Smith-Willis, E. Fenyves and Y. Pan. “Adverse health effects of outdoor air pollutants”. Environment International 32, pp. 815-830, 2006
[3] S.T. Holgate, J.M. Samuel, H.S. Koren and R.L. Maynard. “Air pollution and Health”. Academic Press, New York, 1999.
[4] R. Maynard. “Key airborne pollutants – the impact on health”. Science of the Total Environment 334/335, pp. 9-13, 2004.
[5] R.N., Colvile, E.J. Hutchinson, J.S. Meindell and R.F. Warren. “The transport sector as a source of air pollution”. Atmospheric Environment 35, 1537-1565, 2001.
[6] M. Lewne, J. Cyrys, K. Meliefste, G. Hoek, M. Brauer, P. Fischer, U. Gehring, J. Heinrich, B. Brunekreef and T. Bellander. “Spatial variation in nitrogen dioxide in three European areas”. Science of the Total Environment 332, pp. 217-230, 2004.
[7] DANIEL COOLEY, RICHARD A. DAVIS AND PHILIPPE NAVEAU. “APPROXIMATING THE CONDITIONAL DENSITY GIVEN LARGE OBSERVED VALUES VIA A MULTIVARIATE EXTREMES FRAMEWORK, WITH APPLICATION TO ENVIRONMENTAL DATA”. The Annals of Applied Statistics 2012, vol. 6, No. 4, pp. 1406-1429, 2012 [Jan. 8, 2013].
[8] European Commission. “Position paper on air quality: nitrogen dioxide”, in Working Group on Nitrogen Dioxide, EC, 1997.
[9] WHO (World health Organisation).”Health aspects of air pollution with particulate matter, ozone and nitrogen dioxide”, in Report on a WHO Working Group. Bonn, Germany, pp. 13-15, January 2003.
[10] EPA Fact sheet. “Final Revisions to the national ambient air quality standards for nitrogen dioxide”. Internet: http://www.epa.gov/air/nitrogendioxides/pdfs/20100122fs.pdf, 2010 [Apr. 20, 2015].
[11] Sharma Pragati, Avinash Chandra, S.C. Kaushik, Prateek Sharma and Suresh Jain. “Predicting violations of national ambient air quality standard using extreme value theory for Delhi city”. Atmospheric Pollution Research 3(2012), pp. 170-179, 2012.
[12] Eric Gilleland, Mthieu Ribatet and Alec G. Stephenson. “A software review for extreme value analysis”. Extremes (2013) 16, pp. 103-119, doi: 10.1007/s10687-012-0155-0, 2012.
[13] Zhanling Li, Zhanjie Li, Wei Zhao and Yuehua Wang. “Probability Modeling of Precipitation Extremes over Two River Basins in Northwest of China”. Hindawi Publishing Corporation. Advances in Meteorology, vol. 2015, Article ID 374127, pp. 2-13, Nov. 2015.
[14] Jiafeng Sun. “Heavy-Tailed Longitudinal Data Modelling Using Copulas”. PhD thesis, University of Wisconsin-Madison, 2008.
[15] I.W. Burr. “Cumulative frequency functions”. Annals of Mathematical Statistics 13 (2), pp. 215-232, doi: 10.1214/aoms/1177731607, JSTOR 2235756, 1942.
[16] B. Abbasi, S.Z. Hosseinifard and D.W. Coit. “A neural network applied to estimate Burr XII distribution parameters”. Reliability Engineering and System Safety 95, pp. 647-654, 2010.
[17] D. Ganora, and F. Laio. “Hydrological Applications of the Burr Distribution: Practical Method for Parameter Estimation”. Journal of Hydrological Engineering, vol. 20, issue 11, 10. 1061/(ASCE) HE. 1943-5584.0001203, 04015024, Nov. 2015.
[18] Sexto M., Benjamin, Humberto Vaquera H. and Barry C. Arnold. “Use of the Dagum Distribution for Modelling Tropospheric Ozone levels”. Journal of Environmental Statistics, vol. 5, Issue 5, pp. 1-11, Aug. 2013.
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[20] V.P. Singh, H. Guo and F.X. Yu. ”Parameter estimation for 3-parameter log-logistic distribution (LLD3) by Pome”. Stochastic Hydrol. Hydraul. 7, pp. 163-177, 1993.
[21] W. Jr. Mielke. “Another family of distributions for describing and analyzing precipitation data”. Journal of Applied Meteorology 12, pp. 275-280, 1973.
[22] Quanxi Shao. “Notes on maximum likelihood estimation for the three-parameter Burr XII distribution”. Computational Statistics and Data Analysis 45 (3), pp.675-687, 2004.
[23] C. Kleiber and S. Kotz. “Statistical Size distribution in Economics and Actuarial Sciences”. John Wiley, Hoboken, New Jersey, 2003.
[24] Pandu R. Tadikamalla. “A Look at the Burr and Related Distributions”. International Statistical Review 48 (3), pp. 337-344, doi: 10.2307/1402945, JSTOR 1402945, 1980.
[25] Quanxi Shao. “Estimation for hazardous concentrations based on NOEC toxicity data: an alternative approach”. Environmetrics 11, pp. 583-595, 2000.
[26] M.M. Shoukri, I.U.M. Mian and D.S. Tracy. “Sampling Properties of Estimators of the Log-Logistic Distribution with Application to Canadian Precipitation Data”. The Canadian Journal of Statistics 16 (3), pp. 223-236, doi: 10.2307/3314729, JSTOR 3314729, 1988.
[27] Fahim Ashkar and Smail Mahdi. ”Fitting the log-logistic distribution by generalized moment” Journl of Hydrology 328 (3-4): pp. 694-703, 10.1016/j.jhydrol.2006.01.014.
[28] A. Zempleni (2004). “Goodness-of-fit test in extreme value applications”. Discussion Paper No. 383, SFB 386, Statistische Analyse Diskreter Strukturen, TU Munchen.
[29] WHO (World health Organisation). ”WHO air quality guidelines global update 2005”, in Report on a Working Group Meeting. Bonn, Germany, p. 15, 18-20, Oct. 2005.
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Published
2016-10-25
How to Cite
Thupeng, W. M. (2016). Use of the Three-parameter Burr XII Distribution for Modelling Ambient Daily Maximum Nitrogen Dioxide Concentrations in the Gaborone Fire Brigade. American Scientific Research Journal for Engineering, Technology, and Sciences, 26(2), 18–32. Retrieved from https://asrjetsjournal.org/index.php/American_Scientific_Journal/article/view/1273
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