Search results for "Convolution of probability distributions"

showing 3 items of 3 documents

Bartlett formalism generating functions and Z-transforms in fluctuation and noise theory

1983

Abstract “La theorie des fonctions generatrices s'adapte elle meme et avec la plus grande generalite aux questions des probabilite les plus difficiles.” (Laplace, 1812) “An important part of probability theory consists of the derivation of the probability distribution of the sum of n random variables, each of which obeys a given probability law, and the development of asymptotic forms of these distributions valid for increasing n. Probability generating functions owe their dominant position to the simplification they permit to both problems. Their employment to obtain the successive moments of a probability distribution and to solve the difference equations of probability theory is ancillar…

Generating FunctionPopulation DynamicBartlett formalismMoment-generating functionNoise TheoryConvolution of probability distributionsAlgebra of random variablesStochastic ProceNuclear Energy and EngineeringProbability theoryJoint probability distributionCalculusApplied mathematicsProbability distributionRandom variableSettore ING-IND/19 - Impianti NucleariLaw of the unconscious statisticianMathematicsAnnals of Nuclear Energy
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Radon transform as a set of probability distributions

2009

It is proved that the Radon transform of the Wigner function gives the probability distributions related to measuring the observable operators obtained as linear combinations of position and momentum of the relevant particle. The generalization to an arbitrary number of degrees of freedom is given.

Integral transformsOptical tomographySettore FIS/02 - Fisica Teorica Modelli E Metodi MatematiciRadon transformCharacteristic function (probability theory)Mathematical analysisWigner semicircle distributionCondensed Matter PhysicsConvolution of probability distributionsAtomic and Molecular Physics and OpticsSettore FIS/03 - Fisica Della MateriaRegular conditional probabilityProbability distributionWigner distribution functionQuantum tomographyMathematical PhysicsMathematicsK-distribution
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A characterization of the distribution of a weighted sum of gamma variables through multiple hypergeometric functions

2008

Applying the theory on multiple hypergeometric functions, the distribution of a weighted convolution of Gamma variables is characterized through explicit forms for the probability density function, the distribution function and the moments about the origin. The main results unify some previous contributions in the literature on nite convolution of Gamma distributions. We deal with computational aspects that arise from the representations in terms of multiple hypergeometric functions, introducing a new integral representation for the fourth Lauricella function F (n) D and its con uent form (n) 2 , suitable for numerical integration; some graphics of the probability density function and distr…

Lauricella functionConfluent hypergeometric functionmultiple numerical integration.Applied MathematicsGeneralized gamma distributionMathematical analysisdouble Dirichlet averagecon uent hypergeometric functionMoment-generating functionConvolution of probability distributionsGeneralized hypergeometric functionWeighted Gamma ConvolutionDirichlet averageGeneralized integer gamma distributionApplied mathematicsSettore SECS-S/01 - StatisticaIncomplete gamma functionAnalysisInverse-gamma distributionMathematicsIntegral Transforms and Special Functions
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