A comparison of parameter estimation procedures for experimental bimodal lognormal particle size distributions and grouped data

Abstract

Four estimation methods are compared with regard to the estimated parameters and the resulting estimated moments, when applied to bimodal lognormal particle size distributions. The method of maximum likelihood, of minimum Chi-square and of minimum distance were applied to artificial samples from numerically simulated populations, representative of many aerosol populations found in practice as well as a method derived by the authors, which is based on the binomial distribution of grouped data in diameter intervals. The results of the comparison of estimated and ‘true’ parameters are evaluated in terms of percentage inaccuracies. The expected percentage inaccuracies of the estimated moments calculated fom the estimated parameters are quantified for various physically relevant orders. It is concluded that the maximum likelihood method tends to be preferable to the others.