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# A Bivariate Model for the Distribution of $\sqrt b_1$ and b2

L. R. Shenton and K. O. Bowman
Journal of the American Statistical Association
Vol. 72, No. 357 (Mar., 1977), pp. 206-211
DOI: 10.2307/2286939
Stable URL: http://www.jstor.org/stable/2286939
Page Count: 6
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## 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 $\sqrt b_1$ and b2 is studied, consisting of a Johnson SU approximation to the marginal density of $\sqrt b_1$, and a gamma density for the conditional distribution of b2. Equiprobability contours are given for sampling from normal and nonnormal populations. In the normal case, an eight-parameter model is completely specified.

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