Convenient Beta Distribution Likelihood Techniques for Describing and Comparing Meteorological Data

Paul W. Mielke Jr. Department of Statistics, Colorado State University, Fort Collins 80523

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Abstract

A simple reparameterization of the beta distribution is presented. This reparameterization provides a more intuitive description of the beta distribution than the usual version. As a consequence, easily interpreted beta distribution likelihood ratio tests based on this reparameterization are introduced. To facilitate the use of this approach, convenient iterative procedures are given for obtaining the required maximum likelihood estimates of the relevant parameters. In addition, numerical examples of these techniques are illustrated with recently acquired data from a hail suppression project.

Abstract

A simple reparameterization of the beta distribution is presented. This reparameterization provides a more intuitive description of the beta distribution than the usual version. As a consequence, easily interpreted beta distribution likelihood ratio tests based on this reparameterization are introduced. To facilitate the use of this approach, convenient iterative procedures are given for obtaining the required maximum likelihood estimates of the relevant parameters. In addition, numerical examples of these techniques are illustrated with recently acquired data from a hail suppression project.

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