Positive-part moments via characteristic functions, and more general expressions

Iosif Pinelis ()
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Iosif Pinelis: Michigan Technological University

Journal of Theoretical Probability, 2018, vol. 31, issue 1, 527-555

Abstract: Abstract A unifying and generalizing approach to representations of the positive-part and absolute moments $${{\mathsf {E}}} X_+^p$$ E X + p and $${{\mathsf {E}}}|X|^p$$ E | X | p of a random variable X for real p in terms of the characteristic function (c.f.) of X, as well as to related representations of the c.f. of $$X_+$$ X + , generalized moments $${{\mathsf {E}}} X_+^p e^{iuX}$$ E X + p e i u X , truncated moments, and the distribution function, is provided. Existing and new representations of these kinds are all shown to stem from a single basic representation. Computational aspects of these representations are addressed.

Keywords: Characteristic functions; Positive-part moments; Absolute moments; Truncated moments; Fractional derivatives; Primary 60E10; Secondary 60E07; 62E15; 60E15 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10959-016-0709-1

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