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arXiv:0902.4214 [math.PR]AbstractReferencesReviewsResources

Positive-part moments via the Fourier-Laplace transform

Iosif Pinelis

Published 2009-02-24, updated 2010-01-05Version 2

Integral expressions for positive-part moments 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.

Comments: Accepted for publication in Journal of Theoretical Probability, with Proposition 2.6 downgraded to Example 1. A couple of possible applications are added. Other changes are minor
Categories: math.PR, math.ST, stat.TH
Subjects: 60E10, 42A38, 60E07, 60E15, 42A55, 42A61
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