Chapter 20 Multivariate methods to monitor the risk of critical episodes of environmental contamination using an asymmetric distribution with data of Santiago, Chile

Monitoring the risk of critical episodes of environmental pollution to improve air quality is a big challenge. Santiago of Chile, its capital, is one of the cities with levels of airborne particulate matter contamination that exceed local and international benchmarks. This is due mainly to its location and climate, which provoke critical episodes for human health. In this work, we propose multivariate methods to monitor the risk of such episodes based on levels of PM2.5 and PM10, simultaneously. Fatigue-life distributions are considered to derive these methods, which have shown to have theoretical arguments to model environmental data. We use the Mahalanobis distance and goodness-of-fit tools to evaluate the adequacy of the distributional assumptions. In addition, we use this distance to detect multivariate outliers and conduct a wide discussion about this topic. Multivariate data from the real world are analyzed to model relevant meteorological variables considered in similar studies and to show potential applications. The results reported in this application are in agreement with the critical episodes indicated by the model employed by the Chilean authority.