Abstract
The beta, Johnson's SB, Weibull, lognormal, gamma, and normal distributions are discussed in terms of their flexibility in the skewness squared (β1) − kurtosis (β2) plane. The SB and the beta are clearly the most flexible distributions since they represent surfaces in the plane, whereas the Weibull, lognormal, and gamma are represented by lines, and the normal is represented by a single point.The six distributions are fit to 21 data sets for which both diameters and heights are available. The log likelihood criterion is used to rank the six distributions in regard to their fit to each data set. Overall, Johnson's SB distribution gave the best performance in terms of quality of fit to the variety of sample distributions.
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