  The polygonal distributions are a class of distributions that can be defined
via the mixture of triangular distributions over the unit interval. The class
includes the uniform and trapezoidal distributions, and is an alternative to
the beta distribution. We demonstrate that the polygonal densities are dense in
the class of continuous and concave densities with bounded second derivatives.
Pointwise consistency and Hellinger consistency results for the maximum
likelihood (ML) estimator are obtained. A useful model selection theorem is
stated as well as results for a related distribution that is obtained via the
pointwise square of polygonal density functions.
