The Pearson diagram

The Pearson diagram, Two of its coordinates are the dimensionless indices of skewness1and kurtosis which 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 (B1< 0 and B2<B1+ 1), where no actual distribution of the desired form can exist.Between this critical line B2= B1+ 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 or uni-modal, distributions.