Positive-part moments via the Fourier-Laplace transform
Probability
2017-01-17 v2 Statistics Theory
Statistics Theory
Abstract
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.
Keywords
Cite
@article{arxiv.0902.4214,
title = {Positive-part moments via the Fourier-Laplace transform},
author = {Iosif Pinelis},
journal= {arXiv preprint arXiv:0902.4214},
year = {2017}
}
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