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

Abstract

The use of statistical distributions to predict air quality is valuable for determining the impact of air chemical contaminants on human health. Concentrations of air pollutants are treated as random variables that can be modeled by a statistical distribution that is positively skewed and starts from zero. The type of distribution selected for analyzing air pollution data and its associated parameters depend on factors such as emission source and local meteorology and topography. International environmental guideline use appropriate distributions to compute exceedance probabilities and percentiles for setting administrative targets and issuing environmental alerts. The distribution bears a relationship to the normal distribution, and there are theoretical - and physical-based mechanistic arguments that support its use when analyzing air-pollutant data. Others distribution have also been used to model air population data, such as the beta, exponential, gamma, Johnson, log-logistic, Pearson, and Weibull distribution. One model also developed from physical-mechanistic considerations that has received considerable interest in recent year is the Birnbaum-Saunders distribution. This distribution has theoretical arguments and properties similar to those of the log-normal distribution, which renders it useful for modeling air contamination data. In this review, we have addressed the range of common atmospheric contaminants and the health effects they cause. We have also reviewed the statistical distributions that have been use to model air quality, after which we have detailed the problem of air contamination in Santiago, Chile. We have illustrated a methodology that is based on the Birnbaum-Saunders distributions to analyze air contamination data from Santiago, Chile. Finally, in the conclusions, we have provided a list of synoptic statements designed to help readers understand the significance of air pollution in Chile, and in Santiago, in particular, but that can be useful to other cites and countries.

Multivariate Birnbaum-Saunders Distributions: Modelling and Applications

“…In this illustration, we analyse environmental risk using a multivariate BS quality control chart to monitor urban pollution produced by particulate matter (PM); for further details, see Marchant et al (2013). The data were collected by the Chilean Metropolitan Environmental Health Service and are available at http://sinca.mma.gob.cl.…”

“…The second period (2000)(2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010) includes papers that discuss varied aspects of estimation, modelling and diagnostics, as well as generalizations, computational issues and novel modelling examples, but with justifications still mainly based on an argument of cumulative effects; see, for example, Owen and Padgett (2000); Volodin and Dzhungurova (2000); Tsionas (2001); Rieck (2003); Galea et al (2004); Owen (2006); Xie and Wei (2007); Lemonte et al (2008); Leiva et al (2008Leiva et al ( , 2009); Balakrishnan et al (2009) and Vilca et al (2010). The third period (2011 to the present) is characterized by a new inventiveness, breaking the link with lifetime data analysis and hence extended application in new areas such as: biology, crop yield assessment, econometrics, energy production, forestry, industry, informatics, insurance, inventory management, medicine, psychology, neurology, pollution monitoring, quality control, sociology and seismology; see, for example, Bhatti (2010); Kotz et al (2010); Balakrishnan et al (2011); Leiva et al (2010Leiva et al ( , 2011Leiva et al ( , 2012; Vilca et al (2010); Villegas et al (2011); Azevedo et al (2012); Ferreira et al (2012); Paula et al (2012); Santos-Neto et al (2012; Marchant et al (2013; Saulo et al (2013Saulo et al ( , 2018; Barros et al (2014); …”

Monitoring Environmental Risk by a Methodology Based on Control Charts

“…Such alerts allow human health to be protected, because they address episodes of extreme contamination that need corrective measures. These episodes are manifested by an increment of the incidence and severity of diseases; see Marchant et al [25]. Thus, environmental risk monitoring is important and can be conducted by control charts.…”

“…For this purpose, a number of researchers have utilized the lognormal (LN) distribution for modeling environmental data, mainly due to its physical arguments [29] and its relationship with the normal distribution. However, also the beta, exponential, extreme values, gamma, inverse Gaussian, Johnson SB, log-logistic, Pearson and Weibull distributions have been used for analyzing this kind of data, although without theoretical arguments see Marchant et al [25].…”

A direct analysis of flood interval probability using approximately 100-year streamflow datasets

“…In this paper, we have identified a hydrological analogy in the form of the elapsed times between flood events that also pass a type of threshold. The fatigue life has been used in diverse applications including biological, medical and environmental studies such as air contamination (Sanhueza et al 2008, Marchant et al 2013 and also financial and sharemarket analyses (Ahmed et al 2010) These examples demonstrate the versatility of the fatigue life pd and hence potential application to flood intervals.A more detailed investigation of the fatigue life pd was undertaken using data at gauging station 136202 (Barambah Creek). As evident in Table 2, flood intervals at this location demonstrated the highest preference towards the fatigue life pd (9 out of the 11 ⁄ series).…”