Fitting human exposure data with the Johnson S(B) distribution

Exposure evaluations for epidemiological investigations and risk assessments may require estimates of background concentrations and peak exposures, as well as the population mean and variance. The S(B) distribution is a theoretically appealing probability function for characterizing ratios, and random variables bound by extremes, such as human exposures and environmental concentrations. However, fitting the parameters of this distribution with maximum likelihood methods is often problematic, and some alternative methods are examined here. Two methods based on percentiles, a quantile estimator, and a method-of-moments fitting procedure are explored. The quantile and method-of-moments procedures are based on new explicit expressions for the first four moments of this distribution. The fitting procedures are compared by simulation, and with actual data sets consisting of measurements of human exposure to airborne contaminants.