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The Continuous Hidden Threshold Mixed Skew-Symmetric Distribution

Author

Listed:
  • Bouaddi, Mohammed
  • Belhachemi, Rachid
  • Douch, Mohamed

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.

Suggested Citation

  • Bouaddi, Mohammed & Belhachemi, Rachid & Douch, Mohamed, 2013. "The Continuous Hidden Threshold Mixed Skew-Symmetric Distribution," MPRA Paper 70546, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:70546
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    References listed on IDEAS

    as
    1. M. C. Jones & M. J. Faddy, 2003. "A skew extension of the t‐distribution, with applications," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(1), pages 159-174, February.
    2. Barry Arnold & Robert Beaver & Richard Groeneveld & William Meeker, 1993. "The nontruncated marginal of a truncated bivariate normal distribution," Psychometrika, Springer;The Psychometric Society, vol. 58(3), pages 471-488, September.
    Full references (including those not matched with items on IDEAS)

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    JEL classification:

    • C4 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling

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