Search results for "Complex order moment"

showing 3 items of 3 documents

On the use of fractional calculus for the probabilistic characterization of random variables

2009

In this paper, the classical problem of the probabilistic characterization of a random variable is re-examined. A random variable is usually described by the probability density function (PDF) or by its Fourier transform, namely the characteristic function (CF). The CF can be further expressed by a Taylor series involving the moments of the random variable. However, in some circumstances, the moments do not exist and the Taylor expansion of the CF is useless. This happens for example in the case of $\alpha$--stable random variables. Here, the problem of representing the CF or the PDF of random variables (r.vs) is examined by introducing fractional calculus. Two very remarkable results are o…

Characteristic function (probability theory)FOS: Physical sciencesAerospace EngineeringMathematics - Statistics TheoryOcean EngineeringProbability density functionComplex order momentStatistics Theory (math.ST)Fractional calculusymbols.namesakeIngenieurwissenschaftenFOS: MathematicsTaylor seriesApplied mathematicsCharacteristic function serieMathematical PhysicsCivil and Structural EngineeringMathematicsGeneralized Taylor serieMechanical EngineeringStatistical and Nonlinear PhysicsProbability and statisticsMathematical Physics (math-ph)Condensed Matter PhysicsFractional calculusFourier transformNuclear Energy and EngineeringPhysics - Data Analysis Statistics and ProbabilitysymbolsFractional calculus; Generalized Taylor series; Complex order moments; Fractional moments; Characteristic function series; Probability density function seriesddc:620Series expansionFractional momentProbability density function seriesSettore ICAR/08 - Scienza Delle CostruzioniRandom variableData Analysis Statistics and Probability (physics.data-an)
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CROSS-POWER SPECTRAL DENSITY AND CROSS-CORRELATION REPRESENTATION BY USING FRACTIONAL SPECTRAL MOMENTS

2012

Fractional calculus Mellin transform Complex order moments Fractional moments Fractional spectral moments Cross-correlation function Cross-power spectral density function
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Riesz fractional integrals and complex fractional moments for the probabilistic characterization of random variables

2012

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…

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 variablesProbabilistic Engineering Mechanics
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