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Biometrika 1973 60(3):655-661; doi:10.1093/biomet/60.3.655
© 1973 by Biometrika Trust
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Extended and multivariate Tukey lambda distributions

N. L. JOHNSON and S. KOTZ

University of North Carolina at Chapel Hill
Temple University, Philadelphia, and University of North Carolina at Chapel Hill

The symmetrical Tukey lambda distributions are obtained by simple transformations of a uniformly distributed variable. Systems of multivariate distributions can be formed by applying these transformations to sets of variables having a joint Dirichlet distribution. Since no more than one of such a set of variables can have a uniform distribution, though all have beta distributions, we are led to study distributions of transforms of variables having standard beta distributions. These distributions are termed extended Tukey lambda distributions. Properties of these distributions are studied. Properties of the multivariate distributions are also described and a numerical illustration is presented.

Key Words: Tukey lambda distribution • Beta distribution • Dirichlet distribution • Transformations • Median regression


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