Particle size analysis utilizing grouped data and the log-normal distribution

Abstract The use of the log-normal function in particle size analysis is reviewed and a maximum likelihood method for fitting and testing the fit of a log-normal function to grouped particle size data is described. Since particle size data are usually grouped into size intervals, it is commonly assumed for mathematical purposes that all the particles in a group are equal in size to some mid-size in the interval. This assumption may lead to errors in fitting a function to data. This assumption is avoided by using the grouped data maximum likelihood method. The method is applicable even if the numbers of particles observed in the size groups are small or nil. Also discussed are the statistical tests which may be applied to the fitted parameters of the log-normal function in order to provide estimates of their statistical reliability. A chi-square test is used to justify or discredit the assumption that the data can be considered as a sample from a parent population which is log-normally distributed.