Search results for "Moment-generating function"

showing 6 items of 6 documents

Is there an absolutely continuous random variable with equal probability density and cumulative distribution functions in its support? Is it unique? …

2014

This paper inquires about the existence and uniqueness of a univariate continuous random variable for which both cumulative distribution and density functions are equal and asks about the conditions under which a possible extrapolation of the solution to the discrete case is possible. The issue is presented and solved as a problem and allows to obtain a new family of probability distributions. The different approaches followed to reach the solution could also serve to warn about some properties of density and cumulative functions that usually go unnoticed, helping to deepen the understanding of some of the weapons of the mathematical statistician’s arsenal.

Characteristic function (probability theory)Cumulative distribution functionCalculusProbability mass functionProbability distributionApplied mathematicsProbability density functionMoment-generating functionRandom variableLaw of the unconscious statisticianMathematicsInternational Journal of Advanced Statistics and Probability
researchProduct

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
researchProduct

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
researchProduct

Moment Generating Functions and Central Moments

2018

This section deals with the moment generating functions (m.g.f.) up to sixth order of some discretely defined operators. We mention the m.g.f. and express them in expanded form to obtain moments, which are important in the theory of approximation relevant to problems of convergence.

Section (archaeology)Sixth orderConvergence (routing)Applied mathematicsMoment-generating functionMathematics
researchProduct

Fractional calculus approach to the statistical characterization of random variables and vectors

2009

Fractional moments have been investigated by many authors to represent the density of univariate and bivariate random variables in different contexts. Fractional moments are indeed important when the density of the random variable has inverse power-law tails and, consequently, it lacks integer order moments. In this paper, starting from the Mellin transform of the characteristic function and by fractional calculus method we present a new perspective on the statistics of random variables. Introducing the class of complex moments, that include both integer and fractional moments, we show that every random variable can be represented within this approach, even if its integer moments diverge. A…

Statistics and ProbabilityMellin transformStatistical Mechanics (cond-mat.stat-mech)Characteristic function (probability theory)Multivariate distributionMultivariate random variableMathematical analysisFOS: Physical sciencesMoment-generating functionCondensed Matter PhysicsFractional calculusFractional and complex moments; Multivariate distributions; Power-law tails; Inverse Mellin transformFractional and complex momentIngenieurwissenschaftenApplied mathematicsddc:620Inverse Mellin transformSettore ICAR/08 - Scienza Delle CostruzioniRandom variableCondensed Matter - Statistical MechanicsMathematicsInteger (computer science)Taylor expansions for the moments of functions of random variablesPower-law tail
researchProduct

Stationary and Nontationary Response Probability Density Function of a Beam under Poisson White Noise

2011

In this paper an approximate explicit probability density function for the analysis of external oscillations of a linear and geometric nonlinear simply supported beam driven by random pulses is proposed. The adopted impulsive loading model is the Poisson White Noise , that is a process having Dirac’s delta occurrences with random intensity distributed in time according to Poisson’s law. The response probability density function can be obtained solving the related Kolmogorov-Feller (KF) integro-differential equation. An approximated solution, using path integral method, is derived transforming the KF equation to a first order partial differential equation. The method of characteristic is the…

symbols.namesakeCharacteristic function (probability theory)Cumulative distribution functionMathematical analysissymbolsFirst-order partial differential equationProbability distributionProbability density functionWhite noiseMoment-generating functionPoisson distributionMathematics
researchProduct