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Maximum Likelihood Estimation of Asymmetric Double Type-II Pareto Distributions

Journal of Statistical Theory and Practice, 2020, 14(12).

This paper considers a flexible class of asymmetric double Pareto distributions (ADP) that allows for skewness and asymmetric heavy tails. The cumulative density function is given by,

The inference problem is examined for maximum likelihood. Consistency is proven for the general case when all parameters are unknown. After deriving the Fisher information matrix, asymptotic normality and efficiency are established for a restricted model with the location parameter known. The asymptotic properties of the estimators are then examined using Monte Carlo simulations. To assess its goodness of fit, the ADP is applied to companies’ growth rates, for which it is favored over competing models.

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