Extreme Value Estimation Applied to Aerosol Size Distributions and Related Environmental Problems.

Abstract

This work examines the potential connections between extreme value statistics, problems in aerosol science, and a recent technique of solving ill-posed inversion problems, called EVE (Extreme Value Estimation). EVE estimates functional of the unknown solution by searching the extreme (maximum and minimum) values of that functional within a set of acceptable solutions. The statistics of occurrence of extreme values in real life were not considered when this method was developed. The results of this technique are more con servative than those of the other methods used to solve the problem of aerosol size distribution estimation like non-linear least squares, expectation-maximization, regularization, etc. The utilization of the customary methods of deconvolution may lead to an underestimation of the possibility of occurrence of extreme values in real life. It is suggested that consideration of extreme value statistics might aid in better defining the limits to be placed on the physically acceptable solutions in the EVE deconvolution. Other problems could also benefit from the application of extreme value statistics including the estimation of the second highest value of measured airborne particle mass in the context of the ambient air quality standard for particulate matter less than 10 μm and the determination of the Maximally Exposed Individual as required under the 1990 revisions to the Clean Air Act.