The Pearson diagram

The Pearson diagram, figure 23, requires someexplanation. Two of its coordinates are the dimensionless indices of skewness1and kurtosis2which uniquely characterize the form of the distribution.For example, uniform and normal distributions appear on the(1,2)diagram as the points (0, 1.8) and (0, 3).An exponential distribution on this diagram appears at point (4, 9).A gamma distribution has the form of a straight line, shown as the dot-dashline, extending beyond the two last points.A log-normal distribution is the light solid line below this.The shaded part of the Pearson diagram indicates a critical zone[1< 0 and 2<1+ 1], where no actual distribution of the desired form can exist.Between this critical line 2= 1+ 1 and the line corresponding to gamma functions is the region of beta distributions.This consists of zones for the U-like or bi-modal, and J-like oruni-modal, distributions.