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The First Negative Moment of Skew‐t and Generalized Student′s t‐Distributions in the Principal Value Sense

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  • Chien-Yu Peng

Abstract

The (Cauchy) principal value is a method for assigning values to certain improper integrals which would otherwise be undefined. Using the principal value sense, this study derives an explicit expression of the first negative moment of skew‐t and generalized Student′s t‐distributions for practical applications. Some applications obtained from the FNM of skew‐t and generalized Student′s t‐distributions are also discussed.

Suggested Citation

  • Chien-Yu Peng, 2013. "The First Negative Moment of Skew‐t and Generalized Student′s t‐Distributions in the Principal Value Sense," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnljam:v:2013:y:2013:i:1:n:732875
    DOI: 10.1155/2013/732875
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    References listed on IDEAS

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    1. Peng, Chien-Yu, 2008. "The first negative moment in the sense of the Cauchy principal value," Statistics & Probability Letters, Elsevier, vol. 78(13), pages 1765-1774, September.
    2. Adelchi Azzalini & Antonella Capitanio, 2003. "Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t‐distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 367-389, May.
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