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Maximum Likelihood Estimation of Asymmetric Double Type II Pareto Distributions

PublicationArticle (with peer review)
Daniel Halvarsson, Distribution Theory, Double Pareto Distribution, Firm growth, Maximum Likelihood

Abstract

This paper considers a flexible class of asymmetric double Pareto distributions (ADP) that allows for skewness and asymmetric heavy tails. 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.

Halvarsson, D. (2020). Maximum Likelihood Estimation of Asymmetric Double Type II Pareto Distributions. Journal of Statistical Theory and Practice, 14(22).

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Maximum Likelihood Estimation of Asymmetric Double Type II Pareto Distributions
Artikel (med peer review)Publication
Halvarsson, D.
Publication year

2020

Abstract

This paper considers a flexible class of asymmetric double Pareto distributions (ADP) that allows for skewness and asymmetric heavy tails. 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.

Ratio Working Paper No. 327: Asymmetric Double Pareto Distributions: Maximum Likelihood Estimation with Application to the Growth Rate Distribution of Firms
Working paperPublication
Halvarsson, D.
Publication year

2019

Published in

Ratio Working Paper

Abstract

This paper considers a flexible class of asymmetric double Pareto distributions (ADP) that allows for skewness and asymmetric heavy tails. 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 unequivocally favored over competing models.

Ratio Working Paper No. 327: Asymmetric Double Pareto Distributions: Maximum Likelihood Estimation with Application to the Growth Rate Distribution of Firms
Working paperPublication
Halvarsson, D.
Publication year

2019

Published in

Ratio Working Paper

Abstract

This paper considers a flexible class of asymmetric double Pareto distributions (ADP) that allows for skewness and asymmetric heavy tails. 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 unequivocally favored over competing models.

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