The uniform power distribution

This paper introduces a generalization of the normal distribution: the uniform power distribution. It is a symmetric and unimodal family of distributions, defined on the real line, and is closely related to the exponential power family. The exponential power family was introduced to allow the modelling of kurtosis. The uniform power family matches the exponential power family with respect to the range of kurtosis. However, whereas the exponential is somewhat difficult to work with, the contrary is true for the uniform power family.