Fractional absolute moments of heavy tailed distributions

Abstract

We give methods for calculation of fractional absolute moments with main focus on an infinite variance case with finite mean. We use techniques of fractional differentiation of Laplace transforms or characteristic functions.

The fractional moment errors are evaluated for both prediction and parameter estimation problems.

Keywords

• Fractional absolute moments
• fractional derivatives
• heavy tailed distributions
• characteristic functions
• infinitely divisible distributions