Positive-part moments via the Fourier-Laplace transform
Iosif Pinelis
TL;DR
This paper derives integral formulas for positive-part moments of random variables using Fourier-Laplace transforms, providing conditions for their validity, motivated by applications in extremal probability and statistics.
Contribution
It introduces new integral representations for positive-part moments via Fourier-Laplace transforms along with necessary and sufficient conditions for their validity.
Findings
Provides explicit integral formulas for positive-part moments
Establishes necessary and sufficient conditions for these formulas
Motivated by extremal problems in probability and statistics
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.
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Taxonomy
TopicsProbability and Risk Models · Statistical Distribution Estimation and Applications · Probabilistic and Robust Engineering Design