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Moments of the generalized hyperbolic distribution


  • Scott, David J
  • Würtz, Diethelm
  • Dong, Christine
  • Tran, Thanh Tam


In this paper we demonstrate a recursive method for obtaining the moments of the generalized hyperbolic distribution. The method is readily programmable for numerical evaluation of moments. For low order moments we also give an alternative derivation of the moments of the generalized hyperbolic distribution. The expressions given for these moments may be used to obtain moments for special cases such as the hyperbolic and normal inverse Gaussian distributions. Moments for limiting cases such as the skew hyperbolic t and variance gamma distributions can be found using the same approach.

Suggested Citation

  • Scott, David J & Würtz, Diethelm & Dong, Christine & Tran, Thanh Tam, 2009. "Moments of the generalized hyperbolic distribution," MPRA Paper 19081, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:19081

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    Cited by:

    1. Jose Luis Alayon G., 2015. "Distribucion hiperbolica generalizada: una aplicacion en la seleccion de portafolios y en cuantificacion de medidas de riesgo de mercado," REVISTA DE ECONOMÍA DEL ROSARIO, UNIVERSIDAD DEL ROSARIO, vol. 18(2), pages 249-308, December.

    More about this item


    Generalized hyperbolic distribution; hyperbolic distribution; kurtosis; moments; normal inverse Gaussian distribution; skewed-t distribution; skewness; Student-t distribution.;

    JEL classification:

    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions

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