## 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