Statistics for estimating the population average of a Lifshitz–Slyozov–Wagner (LSW) distribution

A generic version of the Lifshitz–Slyozov–Wagner (LSW) distribution is introduced. Using this generic form, a maximum likelihood (ML) estimator for the population average has been developed. The statistical properties of the estimates obtained by the ML method, as well as the conventional sample average method, have been assessed by Monte Carlo simulations for seven sample sizes ranging from 10 to 1000. Results showed that (i) both estimators yield practically unbiased results, (ii) the standard deviation of estimates obtained by the ML method is significantly less than that of the sample averages, (iii) the distribution of estimates is neither normal, lognormal nor 2-parameter Weibull. Percentage points of the distribution of estimates for both methods have been developed. The use of these points for calculating confidence limits for the population average of the LSW distribution is demonstrated by examples in this article.