  We propose a method based on finite mixture models for classifying a set of
observations into number of different categories. In order to demonstrate the
method, we show how the component densities for the mixture model can be
derived by using the maximum entropy method in conjunction with conservation of
Pythagorean means. Several examples of distributions belonging to the
Pythagorean family are derived. A discussion on estimation of model parameters
and the number of categories is also given.
