A Bivariate Model for the Distribution of √b 1 and b 2

Abstract

In sampling from general populations, the skewness and kurtosis statistics are subject to the constraint b/sub 2/ > 1 + b/sub 1/. A bivariate product-density model for the distribution of ..sqrt..b/sub 1/ and b/sub 2/ is studied, consisting of a Johnson S/sub U/ approximation to the marginal density of ..sqrt..b/sub 1/ a gamma density for the conditional distribution of b/sub 2/. Equiprobability contours are given for sampling from normal and nonnormal populations. In the normal case, an eight-parameter model is completely specified. 4 figures, 4 tables.