Applications of Condition Numbers A-Priori Analysis of Moment Method for Describing Size Distributions.

Abstract

A procedure for estimating the effectiveness of algorithms which retrieve size distribution parameters from cumulative fractions or moments is described. The principle of the algorithm is to select moments, or cumulative fractions, which minimize the condition number. Extensive tests of the algorithm for a distribution consisting of the sum of two log normal distributions were carried out. This procedure can be easily extended to use different numbers and types of constituent functions. The simulations indicated that moment methods which include positive and negative moments give the best result. When the means of the constituent distribution are close, the large condition numbers indicate that no algorithm will give unambiguous values for the parameters.