6533b871fe1ef96bd12d1b4c
RESEARCH PRODUCT
Riesz fractional integrals and complex fractional moments for the probabilistic characterization of random variables
Francesco Paolo PinnolaMario Di Paolasubject
Mellin transformFractional spectral momentDiscretizationCharacteristic function (probability theory)Mechanical EngineeringCharacteristic functionMathematical analysisAerospace EngineeringComplex order momentOcean EngineeringStatistical and Nonlinear PhysicsProbability density functionFractional calculuCondensed Matter PhysicsFractional calculusNuclear Energy and EngineeringProbability density functionApplied mathematicsFractional momentRandom variableCumulantMellin transformCivil and Structural EngineeringMathematicsTaylor expansions for the moments of functions of random variablesdescription
Abstract The aim of this paper is the probabilistic representation of the probability density function (PDF) or the characteristic function (CF) in terms of fractional moments of complex order. It is shown that such complex moments are related to Riesz and complementary Riesz integrals at the origin. By invoking the inverse Mellin transform theorem, the PDF or the CF is exactly evaluated in integral form in terms of complex fractional moments. Discretization leads to the conclusion that with few fractional moments the whole PDF or CF may be restored. Application to the pathological case of an α -stable random variable is discussed in detail, showing the impressive capability to characterize random variables in terms of fractional moments.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2012-07-01 | Probabilistic Engineering Mechanics |