A Bivariate Model for the Distribution of √b₁and b₂

Abstract

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