Exponential Power Distributions

This preliminary set of data is sampled from the exponential power distributions (EPD). The EPD family has the following useful properties:

1. They are parameterized by a single coefficient, alpha, which allows for a continuous setting of the kurtosis.
2. They include the laplace, normal, and (in the limit) uniform distributions.
3. They are uni-modal.

Mathematical Definition

The exponential power distributions are described by the following equation:

The kurtosis of the distribution as a function of alpha is computed as:

Sampled Data

The diamonds in the kurtosis plot below, indicate which densities from the EPD family have been used to generate the uni-modal source data.