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

38 Pages Posted: 24 Feb 2012

Date Written: November 23, 2011

Abstract

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.

Keywords: Exponential Power Distribution, kurtosis, normal standardized Q-Q plot

JEL Classification: C14, C15, C63

Suggested Citation

Coin, Daniele, A Method to Estimate Power Parameter in Exponential Power Distribution Via Polynomial Regression (November 23, 2011). Bank of Italy Temi di Discussione (Working Paper) No. 834, Available at SSRN: https://ssrn.com/abstract=2009894 or http://dx.doi.org/10.2139/ssrn.2009894

Daniele Coin (Contact Author)

Bank of Italy ( email )

Via Nazionale 91
Rome, 00184
Italy

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