Some properties of the tukey g and h family of distributions

The g and h family of distributions, introduced by J.W. Tukey, is generated by a single transformation of the standard normal which allows for symmetry and heavier tails. Selected percentage points are tabulated, and a closed-form solution for the moments, when they exist, is found. A comparison is made with the Pearson system of distributions. The g and h distributions cover most of the Pearson family to an adequate approximation, when the first four moments exist, and also generate a variety of other types of distributions. Selected distributions graphically illustrate the great variety of possible shapes.