Search results for " function"

showing 10 items of 9395 documents

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
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Wait-and-switch stochastic model of the non-Debye relaxation. Derivation of the Burr survival probability

2006

Abstract Stochastic mechanism of relaxation, in which a dipole waits until a favourable condition for reorientation exists, is discussed. Assuming that an imposed direction of a dipole moment may be changed when a migrating defect reaches the dipole, we present a mathematically rigorous scheme relating the local random characteristics of a macroscopic system to its effective relaxation behaviour. We derive a relaxation function (the Burr survival probability) that is characterized by the stretched exponential or the power-law behaviour.

Statistics and ProbabilityMoment (mathematics)DipoleAnomalous diffusionStochastic modellingTransition dipole momentRelaxation (physics)Statistical physicsFunction (mathematics)Condensed Matter PhysicsMathematicsExponential functionPhysica A: Statistical Mechanics and its Applications
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Product and moment formulas for iterated stochastic integrals (associated with Lévy processes)

2019

In this paper, we obtain explicit product and moment formulas for products of iterated integrals generated by families of square integrable martingales associated with an arbitrary Levy process. We...

Statistics and ProbabilityMoment (mathematics)Pure mathematicsMathematics::ProbabilitySquare-integrable functionIterated integralsIterated functionModeling and SimulationProduct (mathematics)Lévy processMathematicsStochastics
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Power and Type I Error of the Mean and Covariance Structure Analysis Model for Detecting Differential Item Functioning in Graded Response Items.

2016

In this simulation study, we investigate the power and Type I error rate of a procedure based on the mean and covariance structure analysis (MACS) model in detecting differential item functioning (DIF) of graded response items with five response categories. The following factors were manipulated: type of DIF (uniform and non-uniform), DIF magnitude (low, medium and large), equality/inequality of latent trait distributions, sample size (100, 200, 400, and 800) and equality or inequality of the sample sizes across groups. The simulated test was made up of 10 items, of which only 1 contained DIF. One hundred replications were generated for each simulated condition. Results indicate that the MA…

Statistics and ProbabilityMultivariate analysisExperimental and Cognitive PsychologyGeneral MedicineCovarianceDifferential item functioningPower (physics)Distribution (mathematics)Arts and Humanities (miscellaneous)Sample size determinationStatisticsItem response theoryType I and type II errorsMathematicsMultivariate behavioral research
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RNA viruses as complex adaptive systems

2004

RNA viruses have high mutation rates and so their populations exist as dynamic and complex mutant distributions. It has been consistently observed that when challenged with a new environment, viral populations adapt following hyperbolic-like kinetics: adaptation is initially very rapid, but then slows down as fitness reaches an asymptotic value. These adaptive dynamics have been explained in terms of populations moving towards the top of peaks on rugged fitness landscapes. Fitness fluctuations of varying magnitude are observed during adaptation. Often the presence of fluctuations in the evolution of physical systems indicates some form of self-organization, or where many components of the s…

Statistics and ProbabilityMutation rateTime FactorsFitness landscapePhysical systemSystems TheoryProbability density functionBiologyVesicular stomatitis Indiana virusGeneral Biochemistry Genetics and Molecular BiologyEvolution MolecularRNA VirusesWeibull distributionGeneticsExperimental evolutionModels StatisticalModels GeneticComputersSystems BiologyApplied MathematicsGeneral MedicineBiological EvolutionSelf-organized criticalityEvolutionary biologyModeling and SimulationMutationAdaptationBiosystems
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Noise-induced resonance-like phenomena in InP crystals embedded in fluctuating electric fields

2016

We explore and discuss the complex electron dynamics inside a low-doped n-type InP bulk embedded in a sub-THz electric field, fluctuating for the superimposition of an external source of Gaussian correlated noise. The results presented in this study derive from numerical simulations obtained by means of a multi-valley Monte Carlo approach to simulate the nonlinear transport of electrons inside the semiconductor crystal. The electronic noise characteristics are statistically investigated by calculating the correlation function of the velocity fluctuations, its spectral density and the integrated spectral density, i.e. the total noise power, for different values of both amplitude and frequenc…

Statistics and ProbabilityNoise powerField (physics)02 engineering and technologyElectron01 natural sciencesNoise (electronics)Settore FIS/03 - Fisica Della MateriaBoltzmann equationsymbols.namesakeCorrelation functionElectric fieldQuantum mechanics0103 physical sciencesstochastic particle dynamics (theory)010306 general physicsfluctuations (theory)Physicstransport properties (theory)Statistical and Nonlinear Physics021001 nanoscience & nanotechnologySettore FIS/07 - Fisica Applicata(Beni Culturali Ambientali Biol.e Medicin)Computational physicsAmplitudeGaussian noisesymbolsStatistics Probability and Uncertainty0210 nano-technologyJournal of Statistical Mechanics: Theory and Experiment
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Gamma Kernel Intensity Estimation in Temporal Point Processes

2011

In this article, we propose a nonparametric approach for estimating the intensity function of temporal point processes based on kernel estimators. In particular, we use asymmetric kernel estimators characterized by the gamma distribution, in order to describe features of observed point patterns adequately. Some characteristics of these estimators are analyzed and discussed both through simulated results and applications to real data from different seismic catalogs.

Statistics and ProbabilityNonparametric statisticsEstimatorKernel principal component analysisPoint processVariable kernel density estimationKernel embedding of distributionsModeling and SimulationKernel (statistics)Bounded domainStatisticsGamma distributionGamma kernel estimatorIntensity functionTemporal point processes.Settore SECS-S/01 - StatisticaMathematicsCommunications in Statistics - Simulation and Computation
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Moments for Some Kumaraswamy Generalized Distributions

2014

Explicit expansions for the moments of some Kumaraswamy generalized (Kw-G) distributions (Cordeiro and de Castro, 2011) are derived using special functions. We explore the Kw-normal, Kw-gamma, Kw-beta, Kw-t, and Kw-F distributions. These expressions are given as infinite weighted linear combinations of well-known special functions for which numerical routines are readily available.

Statistics and ProbabilityNormal distributionSpecial functionsMathematical analysisGeneralized gamma distributionGeneralized beta distributionGeneralized integer gamma distributionLinear combinationInverse distributionVariance-gamma distributionMathematicsCommunications in Statistics - Theory and Methods
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Analisis bayesiano de los contrastes de hipotesis parametricos

1985

Classical solutions to parametric hypothesis testing are shown to be particular instances of the Bayesian solution to a decision problem with two alternatives, in which the increase in utility for rejecting a false null is a linear function of the discrepancy between the accepted parametric model and the more likely model under the null.

Statistics and ProbabilityNull (mathematics)Parametric modelStatistics Probability and UncertaintyDecision problemAlgorithmBayesian solutionLinear functionParametric statisticsMathematicsStatistical hypothesis testingTrabajos de Estadistica Y de Investigacion Operativa
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Dynamics of the Selkov oscillator.

2018

A classical example of a mathematical model for oscillations in a biological system is the Selkov oscillator, which is a simple description of glycolysis. It is a system of two ordinary differential equations which, when expressed in dimensionless variables, depends on two parameters. Surprisingly it appears that no complete rigorous analysis of the dynamics of this model has ever been given. In this paper several properties of the dynamics of solutions of the model are established. With a view to studying unbounded solutions a thorough analysis of the Poincar\'e compactification of the system is given. It is proved that for any values of the parameters there are solutions which tend to inf…

Statistics and ProbabilityPeriodicityQuantitative Biology - Subcellular ProcessesClassical exampleFOS: Physical sciencesDynamical Systems (math.DS)01 natural sciencesModels BiologicalGeneral Biochemistry Genetics and Molecular Biology010305 fluids & plasmassymbols.namesake0103 physical sciencesFOS: MathematicsPhysics - Biological PhysicsMathematics - Dynamical Systems0101 mathematicsSubcellular Processes (q-bio.SC)MathematicsGeneral Immunology and MicrobiologyCompactification (physics)Applied Mathematics010102 general mathematicsMathematical analysisGeneral MedicineMathematical ConceptsKineticsMonotone polygonBiological Physics (physics.bio-ph)FOS: Biological sciencesModeling and SimulationBounded functionOrdinary differential equationPoincaré conjecturesymbolsGeneral Agricultural and Biological SciencesGlycolysisDimensionless quantityMathematical biosciences
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