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May 2016 Fractional absolute moments of heavy tailed distributions
Muneya Matsui, Zbyněk Pawlas
Braz. J. Probab. Stat. 30(2): 272-298 (May 2016). DOI: 10.1214/15-BJPS280


Several convenient methods for calculation of fractional absolute moments are given with application to heavy tailed distributions. Our main focus is on an infinite variance case with finite mean, that is, we are interested in formulae for $\mathbb{E} [\vert X-\mu\vert^{\gamma}]$ with $1<\gamma<2$ and $\mu\in\mathbb{R}$. We review techniques of fractional differentiation of Laplace transforms and characteristic functions. Several examples are given with analytical expressions of $\mathbb{E} [\vert X-\mu\vert^{\gamma}]$. We also evaluate the fractional moment errors for both prediction and parameter estimation problems.


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Muneya Matsui. Zbyněk Pawlas. "Fractional absolute moments of heavy tailed distributions." Braz. J. Probab. Stat. 30 (2) 272 - 298, May 2016.


Received: 1 December 2014; Accepted: 1 January 2015; Published: May 2016
First available in Project Euclid: 31 March 2016

MathSciNet: MR3481104
zbMATH: 1381.60039
Digital Object Identifier: 10.1214/15-BJPS280

Keywords: characteristic functions , Fractional absolute moments , fractional derivatives , heavy tailed distributions , Infinitely divisible distributions

Rights: Copyright © 2016 Brazilian Statistical Association


Vol.30 • No. 2 • May 2016
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