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A method to estimate power parameter in Exponential Power Distribution via polynomial regression

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  • Daniele Coin

    (Bank of Italy)

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.

Suggested Citation

  • Daniele Coin, 2011. "A method to estimate power parameter in Exponential Power Distribution via polynomial regression," Temi di discussione (Economic working papers) 834, Bank of Italy, Economic Research and International Relations Area.
    • Handle: RePEc:bdi:wptemi:td_834_11
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    More about this item

    Keywords

    Exponential Power Distribution; kurtosis; normal standardized Q-Q plot.;
    All these keywords.

    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

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