Description of normal, log—normal and Rosin—Rammler particle populations by a modified version of the beta distribution function

Abstract

Data generated by the normal, log—normal and Rosin—Rammler distribution functions were normalized and fitted with a slightly modified version of the beta distribution function. As long as the frequency function had a zero or practically zero value at the two ends of a finite size range, the fitted curves were, for all practical purposes, indistinguishable from the normal and Rosin—Rammler distributions. The fit of the modified beta function to narrow log—normal distributions was also excellent but it declined significantly as the distribution spread increased. It appears, though, that for real particle populations, having a finite size range, and not necessarily a perfectly smooth size distribution, the modified beta function can replace all three functions, thus providing a way to present and compare the different size distribution patterns in terms of a single mathematical expression.