The new distribution class, Asymmetric Exponential Power Distribution (AEPD), proposed in this paper generalizes the class of Skewed Exponential Power Distributions (SEPD) in a way that in addition to skewness introduces di¤erent decay rates of density in the left and right tails. Our parametrization provides an interpretable role for each parameter. We derive moments and moment-based measures: skewness, kurtosis, expected shortfall. It is demonstrated that a maximum entropy property holds for the AEPD distributions. We establish consistency, asymptotic normality and e¢ ciency of the maximum likelihood estimators over a large part of the parameter space by dealing with the problems created by non-smooth likelihood function and derive explicit analytical expressions of the asymptotic covariance matrix; where the results apply to the SEPD class they enlarge on the current literature. Finally, we give a convenient stochastic representation of the distribution; our Monte Carlo study illustrates the theoretical results.
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Paper provided by McGill University, Department of Economics in its series Departmental Working Papers with number
2007-11.
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Find related papers by JEL classification: C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Estimation C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Econometric and Statistical Methods; Specific Distributions
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