Positive-Part Moments via the Fourier-Laplace Transform

Document Type

Article

Publication Date

6-2011

Department

Department of Mathematical Sciences

Abstract

Integral expressions for positive-part moments E Xp+ (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.

Publication Title

Journal of Theoretical Probability

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