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Positive-Part Moments via the Fourier–Laplace Transform

Journal of Theoretical Probability volume 24, pages 409–421 (2011)Cite this article

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.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Michigan Technological University, Houghton, MI, 49931, USA

    Iosif Pinelis

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  1. Iosif Pinelis
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Correspondence to Iosif Pinelis.

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Supported by NSF grant DMS-0805946

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Pinelis, I. Positive-Part Moments via the Fourier–Laplace Transform. J Theor Probab 24, 409–421 (2011). https://doi.org/10.1007/s10959-010-0276-9

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  • DOI: https://doi.org/10.1007/s10959-010-0276-9

Keywords

  • Positive-part moments
  • Characteristic functions
  • Fourier transforms
  • Fourier–Laplace transforms
  • Integral representations

Mathematics Subject Classification (2000)

  • 60E10
  • 42A38
  • 60E07
  • 60E15
  • 42A55
  • 42A61

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