On evaluating fit of the Lifshitz–Slyozov–Wagner (LSW) distribution to particle size data

Statistical procedures to determine whether particle size data can be characterized by the LSW distribution have been developed by using two methods to estimate the population average: sample mean and maximum likelihood. Two goodness-of-fit tests, namely the Kolmogorov–Smirnov and Anderson–Darling statistics, have been assessed by Monte Carlo simulations for seven sample sizes ranging from 10 to 1000. Results indicate that the fitting method has a profound effect on the critical values of the two tests for all sample sizes. It has also been determined that cut-off (censoring) of the data by finite resolution in microscopy has negligible effect on the evaluation of the fit. Procedures are demonstrated on one dataset from the literature.