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Truncated fractional moments of stable laws

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  • Nolan, John P.

Abstract

Expressions are given for the truncated fractional moments E(X−a)+p of a general stable law. These involve families of special functions that arose out of the study of multivariate stable densities and probabilities. This main result yields expressions for E(X−a)+ when the index of stability α>1, and expressions for fractional absolute and signed moments for any stable law.

Suggested Citation

  • Nolan, John P., 2018. "Truncated fractional moments of stable laws," Statistics & Probability Letters, Elsevier, vol. 137(C), pages 312-318.
    • Handle: RePEc:eee:stapro:v:137:y:2018:i:c:p:312-318
    DOI: 10.1016/j.spl.2018.02.009
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    References listed on IDEAS

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    1. Mittnik, Stefan & Paolella, Marc S. & Rachev, Svetlozar T., 2002. "Stationarity of stable power-GARCH processes," Journal of Econometrics, Elsevier, vol. 106(1), pages 97-107, January.
    2. Abdul-Hamid, Husein & Nolan, John P., 1998. "Multivariate Stable Densities as Functions of One Dimensional Projections," Journal of Multivariate Analysis, Elsevier, vol. 67(1), pages 80-89, October.
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