Beta distributions for particle size having a finite range and predetermined mode, mean or median

The beta distribution function is a flexible model of unimodal particle size distributions that have a finite range. It is especially useful for size reduction and enlargement processes where the size distributions of the entering and leaving particles have opposite skewness. The beta distribution function's main drawback is that its two parameters do not have a clear intuitive meaning, a predicament that can be alleviated by converting one of its parameters into an algebraic term that contains the other and the distribution's mode, mean or median. In this form one can conveniently describe a variety of particle size distributions types and their conversion to others. An interactive program to calculate and plot beta distribution functions with a chosen predetermined mode, mean or median and controlling their spread by a single parameter has been developed and posted on the Internet as a freely downloadable Wolfram Demonstration. [Display omitted] •Beta distributions with predetermined mode, mean or median can be drawn an analyzed.•Wolfram Demonstration allows simulating numerous scenarios in very short time.•The methodology is an effective tool to teach the particle size distributions.•The beta distribution function is an effective model of skewness reversal.