The purpose of this paper is to consider methods which discriminate between 2- and 3-parameter nested alternatives for the gamma, Weibull and log-normal distributions, and to investigate their utility in representing frequency distributions of air pollutant measurements. Monte Carlo experiments are conducted to evaluate the likelihood ratio test, Akaike's information criterion, Schwarz's information criterion, the Chi-square test and the Kolmogorov-Smirnov test. The performance of the tests and criteria depends on the types of nested distributions under consideration, the parametric values of the parent distributions, the confidence levels used (if applicable) and the sample sizes. The practical usefulness of the techniques is illustrated by observing the errors of the models in fitting the upper percentiles of the parent distribution. Two sets of air pollution data, namely hourly pollutant observations of B-scattering and nitrogen dioxide, from an urban airshed are used to examine the similarities and differences in fitting 2- and 3-parameter distributions where historical practice suggests there is a preference for the more parsimonious model.