Transformation and Self-Similarity Properties of Gamma and Weibull Fragment Size Distributions

Abstract

Abstract : This paper describes properties of Gamma and Weibull size distributions, of the type commonly used for liquid and solid fragmentation. Starting with general three-parameter forms, this paper systematically derives, categorizes, and compares two-parameter Gamma and Weibull subsets. Based on comparisons with test data, rare variants may sometimes perform as well as, or better than, well-known variants. Gamma distributions have traditionally been used mostly for liquid fragmentation while Weibull distributions have traditionally been used mostly for solid fragmentation. Based on comparisons with test data, Gamma and Weibull distributions appear to be equally applicable to both liquid and solid fragmentation.