Order Statistics of Air Quality Data

Air pollutant concentrations are inherently random variables because of their dependence on the fluctuations of meteorological and emission variables. We already have seen from Chapter 18 that the concentration predicted by atmospheric diffusion theories is the mean concentration (c). There are important instances in analyzing air pollution where the ability simply to predict the theoretical mean concentration (c) is not enough. Perhaps the most important situation in this regard is in ascertaining compliance with ambient air quality standards. Air quality standards are frequently stated in terms of the number of times per year that a particular concentration level can be exceeded. In order to estimate whether such an exceedance will occur, or how many times it will occur, it is necessary to consider statistical properties of the concentration. One object of this chapter is to develop the tools needed to analyze the statistical character of air quality data. 

Consider the m random unordered variates c(fi), c(f2), , c tm), which are members of the stochastic process c(f,) that generates the time series of available air quality data. If we arrange the data points by order of magnitude, then a new random sequence of ordered variates c -m > c2 m > > cmm is formed. We call ci m the z th highest-order statistic or z th extreme statistic of this random sequence of size m. 

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