Gamma Size Distribution and Stochastic Sampling Errors

Abstract

A maximum likelihood approach to the application of the gamma size distribution is described and compared with the method of moments approach suggested by Ulbrich. Estimation of distribution parameters based on the maximum likelihood principle and Ulbrich's estimation method have different weighting characteristics, which are illustrated through the use of quantile-quantile plots. The ability of the gamma size distribution to describe curvature on a semilogarithmic diagram, and the mathematical simplicity of incorporating it in the sampling error model based on the Poisson process make it possible to derive a sampling error model with consideration given to changes in size distribution shape. It is also shown that variations in size distribution shape can have significant effects on the estimation of sampling errors.