Sampling distributions of surface and mass statistics of a log-normal distribution when estimated by the method of weighted frequencies

Abstract

Theoretical sampling distributions have been derived for surface and mass statistics when they are estimated from a random sample of a log-normal particle size distribution by weighting the frequencies observed at a given size with the corresponding diameter raised to the appropriate power. The theoretical results, which predict a systematic bias of statistics calculated in this way, are compared with computer-generated “experimental” distributions. A method is given for deriving theoretical correction factors with which to adjust the observed median diameters and the adjusted distributions are shown to be very similar to those observed for median diameters calculated from the Hatch-Choate equation. The significance of the results with respect to other distributions is discussed.