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Probability and Statistical Distributions

Željko Ivezi, Andrew J. Connolly, Jacob T. VanderPlas, Alexander Gray, Željko Ivezi, Andrew J. Connolly, Jacob T. VanderPlas, and Alexander Gray

in Statistics, Data Mining, and Machine Learning in Astronomy: A Practical Python Guide for the Analysis of Survey Data

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691151687
eISBN:
9781400848911
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691151687.003.0003
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter reviews notation and basic concepts in probability and statistics. The coverage of various topics cannot be complete, and it is aimed at concepts needed to understand material covered in ... More


Alternative Income Density Models

Fred Campano and Dominick Salvatore

in Income Distribution: Includes CD

Published in print:
2006
Published Online:
May 2006
ISBN:
9780195300918
eISBN:
9780199783441
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0195300912.003.0005
Subject:
Economics and Finance, Development, Growth, and Environmental

Some of the more commonly used models to describe income distribution are explored. These were selected because they have cumulative distribution functions that are invertible and have proven to give ... More


High-Energy Tail of the Velocity Distribution Function

Nikolai V. Brilliantov and Thorsten Pöschel

in Kinetic Theory of Granular Gases

Published in print:
2004
Published Online:
January 2010
ISBN:
9780198530381
eISBN:
9780191713057
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198530381.003.0010
Subject:
Physics, Condensed Matter Physics / Materials

The velocity distribution function of particles whose velocities exceed the thermal velocity cannot be described by a Maxwell distribution. This chapter shows that this part of the velocity ... More


Kinetic Theory of Granular Gases

Nikolai V. Brilliantov and Thorsten Pöschel

Published in print:
2004
Published Online:
January 2010
ISBN:
9780198530381
eISBN:
9780191713057
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198530381.001.0001
Subject:
Physics, Condensed Matter Physics / Materials

Kinetic Theory of Granular Gases provides an introduction to the rapidly developing theory of dissipative gas dynamics — a theory which has mainly evolved over the last decade. The book ... More


Sonine Polynomials Expansion of The Velocity Distribution Function

Nikolai V. Brilliantov and Thorsten Pöschel

in Kinetic Theory of Granular Gases

Published in print:
2004
Published Online:
January 2010
ISBN:
9780198530381
eISBN:
9780191713057
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198530381.003.0007
Subject:
Physics, Condensed Matter Physics / Materials

The velocity distribution of function of a granular gas is different from the Maxwell distribution. It may be represented in the form of a Sonine polynomials expansion. This chapter shows that the ... More


Collective descriptions of beam distributions

J. B. Rosenzweig

in Fundamentals of Beam Physics

Published in print:
2003
Published Online:
January 2010
ISBN:
9780198525547
eISBN:
9780191711725
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198525547.003.0005
Subject:
Physics, Atomic, Laser, and Optical Physics

This chapter generalizes the description of charged particle motion from a single particle viewpoint to one concerned with distributions in phase space. It discusses that the first classes of ... More


Deep Inelastic Scattering

Robin Devenish and Amanda Cooper-Sarkar

Published in print:
2003
Published Online:
January 2010
ISBN:
9780198506713
eISBN:
9780191709562
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198506713.001.0001
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

The book provides a self-contained account of deep inelastic scattering (DIS) in high energy physics. It covers the classic results that lead to the quark-parton model of hadrons and the ... More


FORMAL TRANSPORT THEORY

J. M. Ziman

in Electrons and Phonons: The Theory of Transport Phenomena in Solids

Published in print:
2001
Published Online:
September 2007
ISBN:
9780198507796
eISBN:
9780191709937
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198507796.003.0007
Subject:
Physics, Condensed Matter Physics / Materials

The analysis of the microscopic processes by which electrons and phonons are scattered is only half the calculation of the macroscopic transport coefficients. To discuss the flow of electric and ... More


Random Variables

James Davidson

in Stochastic Limit Theory: An Introduction for Econometricians

Published in print:
1994
Published Online:
November 2003
ISBN:
9780198774037
eISBN:
9780191596117
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198774036.003.0008
Subject:
Economics and Finance, Econometrics

Specializing the concepts of Ch. 7 to the case of real variables, this chapter introduces distribution functions, discrete and continuous distributions, and describes examples such as the binomial, ... More


Kinetic Coefficients and Velocity Distribution for Gases of Elastic Particles

Nikolai V. Brilliantov and Thorsten Pöschel

in Kinetic Theory of Granular Gases

Published in print:
2004
Published Online:
January 2010
ISBN:
9780198530381
eISBN:
9780191713057
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198530381.003.0019
Subject:
Physics, Condensed Matter Physics / Materials

This chapter applies the Chapman–Enskog approach to an inhomogeneous gas of elastic particles. It derives the coefficients of viscosity, thermal conductivity, and velocity distribution function.


An Introduction to Model-Based Survey Sampling with Applications

Ray Chambers and Robert Clark

Published in print:
2012
Published Online:
May 2012
ISBN:
9780198566625
eISBN:
9780191738449
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198566625.001.0001
Subject:
Mathematics, Probability / Statistics

This book is an introduction to the model-based approach to survey sampling. It consists of three parts, with Part I focusing on estimation of population totals. Chapters 1 and 2 introduce survey ... More


REPRINT THE STATISTICAL DYNAMICS OF HOMOGENEOUS TURBULENCE

S. F. Edwards

in Stealing the Gold: A celebration of the pioneering physics of Sam Edwards

Published in print:
2004
Published Online:
September 2007
ISBN:
9780198528531
eISBN:
9780191713415
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198528531.003.0005
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter presents a paper which examines the problem of steady homogeneous isotropic turbulence under idealized conditions, allowing the for the exact form of the correlation functions to be ... More


Analytical solution of the elastic transport equation

Melvin Lax, Wei Cai, and Min Xu

in Random Processes in Physics and Finance

Published in print:
2006
Published Online:
January 2010
ISBN:
9780198567769
eISBN:
9780191718359
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198567769.003.0014
Subject:
Physics, Theoretical, Computational, and Statistical Physics

An example of a random process is the propagation of a particle (or photons, or acoustic wave) in a turbid medium, where particles undergo multiple scattering by randomly distributed scatterers in ... More


Review of probability

Melvin Lax, Wei Cai, and Min Xu

in Random Processes in Physics and Finance

Published in print:
2006
Published Online:
January 2010
ISBN:
9780198567769
eISBN:
9780191718359
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198567769.003.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter reviews probability theory, limiting the discussion to the study of random events as opposed to random processes, the latter being a sequence of random events extended over a period of ... More


Diffuse scattering – thermal, short-range order, gaseous, liquid, and amorphous scattering

Erich H. Kisi and Christopher J. Howard

in Applications of Neutron Powder Diffraction

Published in print:
2008
Published Online:
January 2009
ISBN:
9780198515944
eISBN:
9780191705663
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198515944.003.0010
Subject:
Physics, Condensed Matter Physics / Materials

This chapter deals with diffuse scattering attributable to departures from perfect crystallinity and from gaseous, liquid, or amorphous states. First, the way in which thermal vibration of atoms ... More


Simulating experimental data

Reinhard B. Neder and Thomas Proffen

in Diffuse Scattering and Defect Structure Simulations: A cook book using the program DISCUS

Published in print:
2008
Published Online:
September 2008
ISBN:
9780199233694
eISBN:
9780191715563
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199233694.003.0004
Subject:
Physics, Crystallography

In most cases, simulations of disordered materials are performed to understand experimental observations, in this case diffraction data. This chapter discusses the calculation of several experimental ... More


Kinetic Equations

Nikolai B. Kopnin

in Theory of Nonequilibrium Superconductivity

Published in print:
2001
Published Online:
January 2010
ISBN:
9780198507888
eISBN:
9780191709722
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198507888.003.10
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter derives the kinetic equations for the two-component distribution function in a gauge-invariant form. The collision integrals for interaction of excitations with impurities, phonons, and ... More


Velocity Distribution And Temperature Of A Granular Gas For The Case ε =Const.

Nikolai V. Brilliantov and Thorsten Pöschel

in Kinetic Theory of Granular Gases

Published in print:
2004
Published Online:
January 2010
ISBN:
9780198530381
eISBN:
9780191713057
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198530381.003.0008
Subject:
Physics, Condensed Matter Physics / Materials

For the ε = const the Boltzmann equation may be reduced to a set of two uncoupled equations. One of them describes the evolution of temperature and the other determines the scaled distribution ... More


Velocity Distribution Function and Temperature for Viscoelastic Particles

Nikolai V. Brilliantov and Thorsten Pöschel

in Kinetic Theory of Granular Gases

Published in print:
2004
Published Online:
January 2010
ISBN:
9780198530381
eISBN:
9780191713057
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198530381.003.0009
Subject:
Physics, Condensed Matter Physics / Materials

This chapter shows that for granular gases of viscoelastic particles, the shape of the velocity distribution function cannot be described by a time-dependent function. Instead, it evolves along with ... More


Brownian Motion in Granular Gases

Nikolai V. Brilliantov and Thorsten Pöschel

in Kinetic Theory of Granular Gases

Published in print:
2004
Published Online:
January 2010
ISBN:
9780198530381
eISBN:
9780191713057
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198530381.003.0015
Subject:
Physics, Condensed Matter Physics / Materials

This chapter analyzes Brownian motion in granular gases. Topics discusses include Boltzmann equation for the velocity distribution function of Brownian particles, Fokker–Planck equation for Brownian ... More


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