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The Maximum Likelihood Approach to Probabilistic Modeling of Air Quality Data
Citation:
Fitz-Simons, T. AND D. Holland. The Maximum Likelihood Approach to Probabilistic Modeling of Air Quality Data. U.S. Environmental Protection Agency, Washington, D.C., EPA/600/4-79/044 (NTIS PB80104110).
Description:
Software using maximum likelihood estimation to fit six probabilistic models is discussed. The software is designed as a tool for the air pollution researcher to determine what assumptions are valid in the statistical analysis of air pollution data for the purpose of standard setting, roll-back calculations, estimation of maximum concentrations, threshold approximations, and handling missing observations. The program fits user's data to the normal distribution, the 3-parameter lognormal distribution, the 3-parameter Weibull distribution, the 3-parameter gamma distribution, the Johnson S(B) distribution (a 4-parameter lognormal distribution), and the 4-parameter beta distribution. The parameters are estimated using standard closed solutions to maximizing equations, and a golden section search for all other parameters. Graphical output contains a histogram of the data superimposed by the fitted density for each model. Six goodness-of-fit criteria are supplied and ranked by the program to aid in the selection of the most appropriate choice among the six models. These criteria are absolute deviations, weighted absolute deviations, Kolmogorov-Smirnov statistic, Cramer-von Mises-Smirnov statistic, the log-likelihood function, and the observed significance level of the Chi-square goodness-of-fit test. The results of applying the program to several subsets of the Los Angeles Catalyst Study data base are presented.