Search results for " Complex order moments"

showing 2 items of 2 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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