2011, 1. Aufl., Wiley Series in Probability and Statistics, ISBN 9780470688199, Volume 897, xxvi, 310 pages

The Dirichlet distribution appears in many areas of application, which include modelling of compositional data, Bayesian analysis, statistical genetics, and...

MATHEMATICS | Probability & Statistics | General | Dirichlet problem | Distribution (Probability theory) | Theory of distributions (Functional analysis)

MATHEMATICS | Probability & Statistics | General | Dirichlet problem | Distribution (Probability theory) | Theory of distributions (Functional analysis)

Book

1986, 1, Monographs on statistics and applied probability, ISBN 0412246201, Volume 26., ix, 175

Although there has been a surge of interest in density estimation in recent years, much of the published research has been concerned with purely technical matters with insufficient emphasis given...

ThÃ©orie de l'estimation | Estimation theory | Statistical Theory & Methods

ThÃ©orie de l'estimation | Estimation theory | Statistical Theory & Methods

Book

Combustion and Flame, ISSN 0010-2180, 05/2015, Volume 162, Issue 5, pp. 2006 - 2019

An n-dodecane spray in temperature and pressure conditions typical of diesel engines, known as Spray A, is modelled by the transported probability density function (TPDF...

Diesel | n-Dodecane | Spray A | Transported probability density function | Engine Combustion Network | Ignition | N-Dodecane | ENERGY & FUELS | JET DIFFUSION FLAME | MICROMIXING MODELS | TURBULENT | PDF CALCULATIONS | ENGINEERING, MECHANICAL | ENGINEERING, CHEMICAL | THERMODYNAMICS | ENGINEERING, MULTIDISCIPLINARY | TEMPERATURE | MIXING MODELS | LIFT-OFF LENGTH | ENGINE COMBUSTION | SIMULATIONS | Turbulence | Combustion | Models | Chemical reaction, Rate of | Analysis | Methods

Diesel | n-Dodecane | Spray A | Transported probability density function | Engine Combustion Network | Ignition | N-Dodecane | ENERGY & FUELS | JET DIFFUSION FLAME | MICROMIXING MODELS | TURBULENT | PDF CALCULATIONS | ENGINEERING, MECHANICAL | ENGINEERING, CHEMICAL | THERMODYNAMICS | ENGINEERING, MULTIDISCIPLINARY | TEMPERATURE | MIXING MODELS | LIFT-OFF LENGTH | ENGINE COMBUSTION | SIMULATIONS | Turbulence | Combustion | Models | Chemical reaction, Rate of | Analysis | Methods

Journal Article

Astrophysical Journal, ISSN 0004-637X, 02/2014, Volume 781, Issue 2, pp. 91 - 12

The time evolution of the probability density function (PDF) of the mass density is formulated and solved for systems in free-fall using a simple approximate function for the collapse of a sphere...

gravitation | ISM: clouds | galaxies: star formation | CORES | MOLECULAR CLOUDS | STATISTICS | SUPERSONIC ISOTHERMAL TURBULENCE | STAR-FORMATION | COLUMN DENSITY | GRAVOTURBULENT FRAGMENTATION | DISTRIBUTIONS | ASTRONOMY & ASTROPHYSICS | STELLAR | INITIAL MASS FUNCTION | Collapse | Approximation | Star formation | Mathematical analysis | Evolution | Dynamical systems | Density | Probability density functions | DENSITY | DISTRIBUTION | EVOLUTION | PROBABILITY DENSITY FUNCTIONS | ASTROPHYSICS, COSMOLOGY AND ASTRONOMY | STAR EVOLUTION | APPROXIMATIONS | MASS | GRAVITATION | STARS | GALAXIES | COMPARATIVE EVALUATIONS

gravitation | ISM: clouds | galaxies: star formation | CORES | MOLECULAR CLOUDS | STATISTICS | SUPERSONIC ISOTHERMAL TURBULENCE | STAR-FORMATION | COLUMN DENSITY | GRAVOTURBULENT FRAGMENTATION | DISTRIBUTIONS | ASTRONOMY & ASTROPHYSICS | STELLAR | INITIAL MASS FUNCTION | Collapse | Approximation | Star formation | Mathematical analysis | Evolution | Dynamical systems | Density | Probability density functions | DENSITY | DISTRIBUTION | EVOLUTION | PROBABILITY DENSITY FUNCTIONS | ASTROPHYSICS, COSMOLOGY AND ASTRONOMY | STAR EVOLUTION | APPROXIMATIONS | MASS | GRAVITATION | STARS | GALAXIES | COMPARATIVE EVALUATIONS

Journal Article

Journal of power sources, ISSN 0378-7753, 2013, Volume 232, pp. 209 - 218

A new method, probability density function (PDF), is proposed for evaluating the state of health (SOH...

Probability density function | Lithium-ion battery | Statistical frequency | Cycle life | State of health | ELECTROCHEMISTRY | CAPACITY | ENERGY & FUELS | MATERIALS SCIENCE, MULTIDISCIPLINARY | CHEMISTRY, PHYSICAL | ELECTRODE | POWER | Analysis | Algorithms | Batteries

Probability density function | Lithium-ion battery | Statistical frequency | Cycle life | State of health | ELECTROCHEMISTRY | CAPACITY | ENERGY & FUELS | MATERIALS SCIENCE, MULTIDISCIPLINARY | CHEMISTRY, PHYSICAL | ELECTRODE | POWER | Analysis | Algorithms | Batteries

Journal Article

The Astrophysical Journal Letters, ISSN 2041-8205, 01/2011, Volume 727, Issue 1, p. L21

We examine the relation between the density variance and the mean-square Mach number in supersonic, isothermal turbulence, assumed in several recent analytic models of the star formation process...

Magnetohydrodynamics (MHD) | Shock waves | Hydrodynamics | Turbulence | Stars: formation | ISM: structure | 2D OBSERVATIONS | CLOUD COMPLEXES | STATISTICS | hydrodynamics | turbulence | stars: formation | FIELD EXTINCTION MAPS | ASTRONOMY & ASTROPHYSICS | GAS | DYNAMICS | PROBABILITY-DISTRIBUTION FUNCTIONS | INITIAL MASS FUNCTION | INTERSTELLAR TURBULENCE | NUMERICAL SIMULATIONS | magnetohydrodynamics (MHD) | shock waves | Physics - Astrophysics of Galaxies | DIMENSIONLESS NUMBERS | VELOCITY | HYDRODYNAMICS | MAGNETOHYDRODYNAMICS | FUNCTIONS | SHOCK WAVES | DENSITY | MACH NUMBER | DISTRIBUTION FUNCTIONS | PROBABILITY | FLUID MECHANICS | MECHANICS | EVOLUTION | ASTROPHYSICS, COSMOLOGY AND ASTRONOMY | STAR EVOLUTION | CLOUDS | PHYSICAL PROPERTIES | TURBULENCE

Magnetohydrodynamics (MHD) | Shock waves | Hydrodynamics | Turbulence | Stars: formation | ISM: structure | 2D OBSERVATIONS | CLOUD COMPLEXES | STATISTICS | hydrodynamics | turbulence | stars: formation | FIELD EXTINCTION MAPS | ASTRONOMY & ASTROPHYSICS | GAS | DYNAMICS | PROBABILITY-DISTRIBUTION FUNCTIONS | INITIAL MASS FUNCTION | INTERSTELLAR TURBULENCE | NUMERICAL SIMULATIONS | magnetohydrodynamics (MHD) | shock waves | Physics - Astrophysics of Galaxies | DIMENSIONLESS NUMBERS | VELOCITY | HYDRODYNAMICS | MAGNETOHYDRODYNAMICS | FUNCTIONS | SHOCK WAVES | DENSITY | MACH NUMBER | DISTRIBUTION FUNCTIONS | PROBABILITY | FLUID MECHANICS | MECHANICS | EVOLUTION | ASTROPHYSICS, COSMOLOGY AND ASTRONOMY | STAR EVOLUTION | CLOUDS | PHYSICAL PROPERTIES | TURBULENCE

Journal Article

Journal of fluid mechanics, ISSN 0022-1120, 03/2019, Volume 862, pp. 449 - 489

...). In the present work, we tackle the problem of developing a framework for the stochastic modelling of moderately dense particle-laden flows, based on a Lagrangian probability-density-function formalism...

JFM Papers | particle/fluid flow | multiphase flow | turbulence modelling | MECHANICS | PHYSICS, FLUIDS & PLASMAS | DISPERSION | MECHANISMS | EQUATION | Turbulent flow | Segregation | Fluid flow | Decomposition | Density | Phase velocity | Energy | Clusters | Isotropic turbulence | Modelling | Mathematical models | Coupling | Framework | Two fluid models | Turbulence | Computer simulation | Computational fluid dynamics | Particle collisions | Probability theory | Momentum | Velocity | Turbulence models | Stochasticity | Stochastic models | Formalism

JFM Papers | particle/fluid flow | multiphase flow | turbulence modelling | MECHANICS | PHYSICS, FLUIDS & PLASMAS | DISPERSION | MECHANISMS | EQUATION | Turbulent flow | Segregation | Fluid flow | Decomposition | Density | Phase velocity | Energy | Clusters | Isotropic turbulence | Modelling | Mathematical models | Coupling | Framework | Two fluid models | Turbulence | Computer simulation | Computational fluid dynamics | Particle collisions | Probability theory | Momentum | Velocity | Turbulence models | Stochasticity | Stochastic models | Formalism

Journal Article

Climate dynamics, ISSN 1432-0894, 2017, Volume 50, Issue 1-2, pp. 31 - 49

...â€”the N-dimensional probability density function transformâ€”is adapted for use as a multivariate bias correction algorithm (MBCn...

Climatology | Bias correction | Earth Sciences | Precipitation | Quantile mapping | Post-processing | Climate model | Geophysics/Geodesy | Oceanography | Model output statistics | Fire weather | Multivariate | CHANGING CLIMATE | PERFORMANCE | DEPENDENCE | OUTPUTS | IMPACT | TEMPERATURE | EXTREMES | SCALES | METEOROLOGY & ATMOSPHERIC SCIENCES | Usage | Climate models | Forecasts and trends | Models | Precipitation variability | Climatic analysis | Correlation | Climate | Image processing | Atmospheric models | Bias | Mapping | Maxima | Probability density functions | Forest fires | Colour | Case studies | Risks | Variables | Probability density function | Mathematical models | Modelling | Quantiles | Wildfires | Computer simulation | Probability theory | Regional analysis | Rainfall | Data processing | Forecasting | Climate change | Fields | Algorithms | Regional climates | Distribution | Fire | Autocorrelation

Climatology | Bias correction | Earth Sciences | Precipitation | Quantile mapping | Post-processing | Climate model | Geophysics/Geodesy | Oceanography | Model output statistics | Fire weather | Multivariate | CHANGING CLIMATE | PERFORMANCE | DEPENDENCE | OUTPUTS | IMPACT | TEMPERATURE | EXTREMES | SCALES | METEOROLOGY & ATMOSPHERIC SCIENCES | Usage | Climate models | Forecasts and trends | Models | Precipitation variability | Climatic analysis | Correlation | Climate | Image processing | Atmospheric models | Bias | Mapping | Maxima | Probability density functions | Forest fires | Colour | Case studies | Risks | Variables | Probability density function | Mathematical models | Modelling | Quantiles | Wildfires | Computer simulation | Probability theory | Regional analysis | Rainfall | Data processing | Forecasting | Climate change | Fields | Algorithms | Regional climates | Distribution | Fire | Autocorrelation

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 01/2016, Volume 305, pp. 817 - 837

In this paper we address the problem of computing the numerical solution to kinetic partial differential equations involving many phase variables. These types...

Uncertainty quantification | Proper generalized decomposition | ANOVA decomposition | Kinetic partial differential equations | High-order numerical methods | Stochastic dynamical systems | DECOMPOSITION | GENERALIZED POLYNOMIAL CHAOS | ALGORITHMS | PHYSICS, MATHEMATICAL | PDF EQUATIONS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | ANOVA EXPANSIONS | Algorithms | Specific gravity | Analysis | Methods | Partial differential equations | Computation | Mathematical analysis | Mathematical models | Dynamical systems | Analysis of variance | Probability density functions | FOKKER-PLANCK EQUATION | PROBABILITY | SERIES EXPANSION | NUMERICAL SOLUTION | PROBABILITY DENSITY FUNCTIONS | STOCHASTIC PROCESSES | NONLINEAR PROBLEMS | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | PROBABILISTIC ESTIMATION | BOLTZMANN EQUATION

Uncertainty quantification | Proper generalized decomposition | ANOVA decomposition | Kinetic partial differential equations | High-order numerical methods | Stochastic dynamical systems | DECOMPOSITION | GENERALIZED POLYNOMIAL CHAOS | ALGORITHMS | PHYSICS, MATHEMATICAL | PDF EQUATIONS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | ANOVA EXPANSIONS | Algorithms | Specific gravity | Analysis | Methods | Partial differential equations | Computation | Mathematical analysis | Mathematical models | Dynamical systems | Analysis of variance | Probability density functions | FOKKER-PLANCK EQUATION | PROBABILITY | SERIES EXPANSION | NUMERICAL SOLUTION | PROBABILITY DENSITY FUNCTIONS | STOCHASTIC PROCESSES | NONLINEAR PROBLEMS | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | PROBABILISTIC ESTIMATION | BOLTZMANN EQUATION

Journal Article

Combustion and flame, ISSN 0010-2180, 2018, Volume 193, pp. 344 - 362

.... One challenge is to find functions that can reproduce the joint probability density function (PDF...

Direct numerical simulation | Multiscalar turbulent mixing | Presumed probability density function | COMBUSTION | ENERGY & FUELS | FRACTION FLAMELET MODEL | ISOTROPIC TURBULENCE | HOT-COFLOW | DIRICHLET DISTRIBUTION | ENGINEERING, MECHANICAL | PASSIVE SCALAR | ENGINEERING, CHEMICAL | THERMODYNAMICS | ENGINEERING, MULTIDISCIPLINARY | LARGE-EDDY SIMULATION | REACTING FLOWS | PREMIXED JET BURNER | NUMERICAL SIMULATIONS | Turbulence | Combustion | Distribution (Probability theory) | Numerical analysis | Analysis | Aerospace engineering

Direct numerical simulation | Multiscalar turbulent mixing | Presumed probability density function | COMBUSTION | ENERGY & FUELS | FRACTION FLAMELET MODEL | ISOTROPIC TURBULENCE | HOT-COFLOW | DIRICHLET DISTRIBUTION | ENGINEERING, MECHANICAL | PASSIVE SCALAR | ENGINEERING, CHEMICAL | THERMODYNAMICS | ENGINEERING, MULTIDISCIPLINARY | LARGE-EDDY SIMULATION | REACTING FLOWS | PREMIXED JET BURNER | NUMERICAL SIMULATIONS | Turbulence | Combustion | Distribution (Probability theory) | Numerical analysis | Analysis | Aerospace engineering

Journal Article

Journal of climate, ISSN 0894-8755, 3/2014, Volume 27, Issue 5, pp. 2087 - 2108

A unified turbulence and cloud parameterization based on multivariate probability density functions (PDFs...

Precipitation | Liquids | Clouds | Aerosols | Stratocumulus clouds | Ice | Parameterization | Microphysics | Convection | Convection clouds | BOUNDARY-LAYER CLOUDS | IMAGING SPECTRORADIOMETER MISR | PART I | General circulation models | LARGE-SCALE MODELS | STRATIFORM CLOUD MICROPHYSICS | SINGLE-COLUMN | PDF-BASED MODEL | INTERCOMPARISON PROJECT | INCLUDING MASS FLUXES | Model evaluation/performance | UNIFIED PARAMETERIZATION | METEOROLOGY & ATMOSPHERIC SCIENCES | Cloud parameterizations | Probability | Meteorology | Parametrization | Atmospheric General Circulation Models | Dynamics | Activation | Probability density functions

Precipitation | Liquids | Clouds | Aerosols | Stratocumulus clouds | Ice | Parameterization | Microphysics | Convection | Convection clouds | BOUNDARY-LAYER CLOUDS | IMAGING SPECTRORADIOMETER MISR | PART I | General circulation models | LARGE-SCALE MODELS | STRATIFORM CLOUD MICROPHYSICS | SINGLE-COLUMN | PDF-BASED MODEL | INTERCOMPARISON PROJECT | INCLUDING MASS FLUXES | Model evaluation/performance | UNIFIED PARAMETERIZATION | METEOROLOGY & ATMOSPHERIC SCIENCES | Cloud parameterizations | Probability | Meteorology | Parametrization | Atmospheric General Circulation Models | Dynamics | Activation | Probability density functions

Journal Article

Renewable Energy, ISSN 0960-1481, 01/2018, Volume 115, pp. 1260 - 1280

Probability density functions (PDFs) are normally used to describe wind speed distribution for the proper selection of wind turbines in a given location...

Probability density function | Renewable energy | Wind speed | Normal distribution | Mixture distribution | Goodness of fit | GREEN & SUSTAINABLE SCIENCE & TECHNOLOGY | ENERGY OUTPUT | MODELS | ENERGY & FUELS | POWER | WEIBULL | Usage | Distribution (Probability theory) | Alternative energy sources | Air-turbines | Analysis

Probability density function | Renewable energy | Wind speed | Normal distribution | Mixture distribution | Goodness of fit | GREEN & SUSTAINABLE SCIENCE & TECHNOLOGY | ENERGY OUTPUT | MODELS | ENERGY & FUELS | POWER | WEIBULL | Usage | Distribution (Probability theory) | Alternative energy sources | Air-turbines | Analysis

Journal Article