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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)

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    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.

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    File URL: http://www.bancaditalia.it/pubblicazioni/econo/temidi/td11/td834_11/en_td834/en_tema_834.pdf
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    Bibliographic Info

    Paper provided by Bank of Italy, Economic Research and International Relations Area in its series Temi di discussione (Economic working papers) with number 834.

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    Date of creation: Nov 2011
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    Handle: RePEc:bdi:wptemi:td_834_11

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    Related research

    Keywords: Exponential Power Distribution; kurtosis; normal standardized Q-Q plot.;

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