The Continuous Hidden Threshold Mixed Skew-Symmetric Distribution

MPRA Paper No. 71002

37 Pages Posted: 15 Sep 2016 Last revised: 10 Nov 2017

See all articles by Mohammed Bouaddi

Mohammed Bouaddi

The American University in Cairo

Rachid Belhachemi

Independent

Mohamed Douch

RMCC Management and Economics Dept; RMC Canada

Date Written: December 1, 2015

Abstract

This paper explores a way to construct a new family of univariate probability distributions where the parameters of the distribution capture the dependence between the variable of interest and the continuous latent state variable (the regime). The distribution nests two well known families of distributions, namely, the skew normal family of Azzalini (1985) and a mixture of two Arnold et al. (1993) distribution. We provide a stochastic representation of the distribution which enables the user to easily simulate the data from the underlying distribution using generated uniform and normal variates. We also derive the moment generating function and the moments. The distribution comprises eight free parameters that make it very flexible. This flexibility allows the user to capture many stylized facts about the data such as the regime dependence, the asymmetry and fat tails as well as thin tails.

Keywords: Continuous Hidden Threshold, Mixture Distribution, Skew-Symmetric Distribution, Split Distribution

JEL Classification: C4, C46, C6

Suggested Citation

Bouaddi, Mohammed and Belhachemi, Rachid and Douch, Mohamed MD, The Continuous Hidden Threshold Mixed Skew-Symmetric Distribution (December 1, 2015). MPRA Paper No. 71002, Available at SSRN: https://ssrn.com/abstract=2839022 or http://dx.doi.org/10.2139/ssrn.2839022

Mohammed Bouaddi

The American University in Cairo ( email )

P.O. Box 2511
Cairo
Egypt

Rachid Belhachemi

Independent ( email )

Mohamed MD Douch (Contact Author)

RMCC Management and Economics Dept ( email )

P.O. Box 17,000, Station Forces
Kingston, ON K7K 7B4
Canada

RMC Canada ( email )

P.O. Box 17,000, Station Forces
Kingston, ON K7K 7B4
Canada

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