A Method to Estimate Power Parameter in Exponential Power Distribution Via Polynomial Regression

The Exponential Power Distribution (EPD), also known as Generalized Error Distribution (GED), is a flexible symmetrical unimodal family belonging to the exponential family. The EPD becomes the density function of a range of symmetric distributions with different values of its power parameter B. A closed-form estimator for B does not exist, so the power parameter is usually estimated numerically. Unfortunately the optimization algorithms do not always converge, especially when the true value of B is close to its parametric space frontier. In this paper we present an alternative method for estimating B, based on the Normal Standardized Q-Q Plot and exploiting the relationship between B and the kurtosis. It is a direct method that does not require computational efforts or the use of optimization algorithms