Modeling distributions of air pollutant concentrations—II. Estimation of one and two parameter statistical distributions

Abstract In Part I of this series Taylor, Jakeman and Simpson (1986, Atmospheric Environment , 20 , 1781–1789) examined the problem of identifying the appropriate distributional form for air pollution concentration data. In this paper we examine the parameter estimation problem. Monte Carlo simulation is used to compare methods for fitting statistical distributions to such data where the distributional form is known. Three methods are investigated for estimating the parameters of the lognormal distribution, two methods for the exponential distribution, three methods for the γ-distribution and four methods for the Weibull distribution. For all distributions and for each method we examine the accuracy with which the upper percentiles of the distribution are evaluated as it is these percentiles which are referred to by air quality standards. For each distribution a simple empirical model, which yields approximations to the relative root mean square error of the percentile estimates against sample size and parameter values, is developed and demonstrated. Thus for each distributional model an estimate of the relative error associated with evaluating high pollutant levels may be readily determined.