A method to estimate power parameter in exponential power distribution via polynomial regression

The exponential power distribution (EPD), also known as generalized error distribution, is a flexible symmetrical unimodal family that belongs to the exponential one. The EPD becomes the density function of a range of symmetric distributions with different values of its power parameter β. A closed-form estimator for β 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 β is close to its parametric space frontier. In this paper, we present an alternative method to estimate β. Our proposal is based on the normal standardized Q–Q plot, and it exploits the relationship between β and the kurtosis. Furthermore, it is a direct method which does not require computational efforts nor the use of optimization algorithms.