Point process statistics improves particle size analysis

Abstract

This paper re-considers the foundations of particle size statistics. While traditional particle size statistics consider their data as samples of random variables and use methods of classical mathematical statistics, here a particle sample is treated as a point process sample, and a suitable form of statistics is recommended. The whole sequence of ordered particle sizes is considered as a random variable in a suitable sample space. Instead of distribution functions, point process intensity functions are used. The application of point process data analysis is demonstrated for samples of fragments from single-particle crushing of glass balls. Three cases of data handling with point processes are presented: statistics for oversize particles, pooling of independent particle samples and pooling of piecewise particle data. Finally, the problem of goodness-of-fit testing for particle samples is briefly discussed. The point process approach turns out to be an extension of the classical approach, is simpler and more elegant, but retains all valuable traditional ideas. It is particularly strong in the analysis of oversize particles.