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Positive-Part Moments via the Fourier–Laplace Transform

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  • Iosif Pinelis

    (Michigan Technological University)

Abstract

Integral expressions for positive-part moments $\mathsf{E}\,X_{+}^{p}$ (p>0) of random variables X are presented, in terms of the Fourier–Laplace or Fourier transforms of the distribution of X. A necessary and sufficient condition for the validity of such an expression is given. This study was motivated by extremal problems in probability and statistics, where one needs to evaluate such positive-part moments.

Suggested Citation

  • Iosif Pinelis, 2011. "Positive-Part Moments via the Fourier–Laplace Transform," Journal of Theoretical Probability, Springer, vol. 24(2), pages 409-421, June.
    • Handle: RePEc:spr:jotpro:v:24:y:2011:i:2:d:10.1007_s10959-010-0276-9
    DOI: 10.1007/s10959-010-0276-9
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    References listed on IDEAS

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    1. V. Bentkus, 2003. "An Inequality for Tail Probabilities of Martingales with Differences Bounded from One Side," Journal of Theoretical Probability, Springer, vol. 16(1), pages 161-173, January.
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    Cited by:

    1. Iosif Pinelis, 2018. "Positive-part moments via characteristic functions, and more general expressions," Journal of Theoretical Probability, Springer, vol. 31(1), pages 527-555, March.

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