A method to estimate power parameter in Exponential Power Distribution via polynomial regression
AbstractThe 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.
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Bibliographic InfoPaper provided by Bank of Italy, Economic Research and International Relations Area in its series Temi di discussione (Economic working papers) with number 834.
Date of creation: Nov 2011
Date of revision:
Exponential Power Distribution; kurtosis; normal standardized Q-Q plot.;
Find related papers by JEL classification:
- C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
- C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
- C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-12-19 (All new papers)
- NEP-ECM-2011-12-19 (Econometrics)
- NEP-ETS-2011-12-19 (Econometric Time Series)
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