STATISTICAL ANALYSIS OF BUBBLE AND CRYSTAL SIZE DISTRIBUTIONS: FORMULATIONS AND PROCEDURES

Abstract

Bubble and crystal size distributions have previously been described only by either exponential or power law functions. Within this limited framework, it has not been possible to characterize size distributions in a fully quantitative manner. We have developed an analytical and computational formulation with which to characterize and study crystal and bubble size distributions (BSD). This formulation demonstrates that all distributions known to date belong to the logarithmic family of statistical distributions. Four functions within the logarithmic family are best suited to natural bubbles and crystals (log normal, logistic, Weibull, and exponential). This characterization is supported by the fact that the power law function widely used for crystal and bubble size analysis is not a statistical distribution function, but rather represents an approximation of the upper regions (larger bubbles/crystals) of the logistic distribution, whose sizes are much larger than the mode.