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Cumulative Distribution Function - Probability
Cumulative Distribution Function - Probability
Published: 2012/02/11
Channel: Engineer Clearly
The Probability Distribution Function (PDF) of [X]
The Probability Distribution Function (PDF) of [X]
Published: 2014/02/26
Channel: MIT OpenCourseWare
Probability density functions | Probability and Statistics | Khan Academy
Probability density functions | Probability and Statistics | Khan Academy
Published: 2009/02/16
Channel: Khan Academy
Constructing a probability distribution for random variable | Khan Academy
Constructing a probability distribution for random variable | Khan Academy
Published: 2014/02/07
Channel: Khan Academy
Calculating a Cumulative Distribution Function (CDF)
Calculating a Cumulative Distribution Function (CDF)
Published: 2014/02/26
Channel: MIT OpenCourseWare
Probability Mass Function & Density Function in Hindi
Probability Mass Function & Density Function in Hindi
Published: 2015/05/15
Channel: Bhagwan Singh Vishwakarma
Continuous Random Variables: Cumulative Distribution Functions
Continuous Random Variables: Cumulative Distribution Functions
Published: 2012/11/27
Channel: MrNichollTV
Cumulative Distribution Function : Example : ExamSolutions
Cumulative Distribution Function : Example : ExamSolutions
Published: 2009/12/05
Channel: ExamSolutions
Probability Density Functions / Continuous Random Variables
Probability Density Functions / Continuous Random Variables
Published: 2009/06/26
Channel: patrickJMT
Binomial CDF (Cumulative Distribution Function) on TI-83 & TI-84
Binomial CDF (Cumulative Distribution Function) on TI-83 & TI-84
Published: 2015/08/23
Channel: OpenIntroOrg
The Amazing Normal Distribution Function
The Amazing Normal Distribution Function
Published: 2006/09/09
Channel: k0x
Cumulative distribution function technique
Cumulative distribution function technique
Published: 2016/03/10
Channel: Lawrence Leemis
Gaussian
Gaussian
Published: 2012/12/12
Channel: Paul Francis
Cumulative Distribution Function
Cumulative Distribution Function
Published: 2012/06/13
Channel: David Waldo
Probability : Cumulative Distribution Function F(X) : ExamSolutions
Probability : Cumulative Distribution Function F(X) : ExamSolutions
Published: 2011/04/14
Channel: ExamSolutions
Section 5 1 Distribution Function Technique
Section 5 1 Distribution Function Technique
Published: 2017/04/19
Channel: Karen Benway
probability density functions and cumulative distribution functions s1
probability density functions and cumulative distribution functions s1
Published: 2013/02/14
Channel: Rhys Steele
Cumulative Distribution Functions : Introduction : ExamSolutions
Cumulative Distribution Functions : Introduction : ExamSolutions
Published: 2009/12/04
Channel: ExamSolutions
Finding a CDF from a pdf
Finding a CDF from a pdf
Published: 2015/11/26
Channel: Mr Camilleri
PDF and CDF Explanations
PDF and CDF Explanations
Published: 2011/04/21
Channel: UAMath115
Discrete Random Variables 1) Brief Intro   Probability Distribution and Function
Discrete Random Variables 1) Brief Intro Probability Distribution and Function
Published: 2013/08/26
Channel: ukmathsteacher
Method of Distribution Functions 1
Method of Distribution Functions 1
Published: 2014/11/03
Channel: Matthew Jones
Mod-01 Lec-16 CUMULATIVE DISTRIBUTION FUNCTION
Mod-01 Lec-16 CUMULATIVE DISTRIBUTION FUNCTION
Published: 2015/02/19
Channel: nptelhrd
Introduction to discrete probability distributions
Introduction to discrete probability distributions
Published: 2012/12/07
Channel: Khan Academy
Discrete Random Variables 2)   Cumulative Distribution Function
Discrete Random Variables 2) Cumulative Distribution Function
Published: 2013/08/26
Channel: ukmathsteacher
Lecture - 5 Probability Distributions and Density Functions
Lecture - 5 Probability Distributions and Density Functions
Published: 2008/07/10
Channel: nptelhrd
Optics 2: Validity of Wigner Distribution Function for Ray-based Imaging
Optics 2: Validity of Wigner Distribution Function for Ray-based Imaging
Published: 2011/04/13
Channel: cmurobotics
Orbitals: Nodes and Radial Distribution Function
Orbitals: Nodes and Radial Distribution Function
Published: 2017/02/25
Channel: Chemistry_OK OSU
Cumulative Distribution Function of an Order Statistic
Cumulative Distribution Function of an Order Statistic
Published: 2014/10/06
Channel: Ben Garside
Uniform distribution cumulative distribution function
Uniform distribution cumulative distribution function
Published: 2016/02/12
Channel: Lawrence Leemis
Features of the Fermi Dirac Distribution Function
Features of the Fermi Dirac Distribution Function
Published: 2011/09/20
Channel: nptelhrd
The Binomial Distribution / Binomial Probability Function
The Binomial Distribution / Binomial Probability Function
Published: 2009/05/06
Channel: patrickJMT
Python tutorial: Cumulative Distribution Functions
Python tutorial: Cumulative Distribution Functions
Published: 2016/11/09
Channel: DataCamp
Properties of the probability distribution function
Properties of the probability distribution function
Published: 2014/11/03
Channel: Jochumzen
Normal distribution
Normal distribution's probability density function derived in 5min
Published: 2013/08/22
Channel: acadelivery
Chemistry - Electron Structures in Atoms (26 of 40) Radial Probability Density Function: S-Orbital
Chemistry - Electron Structures in Atoms (26 of 40) Radial Probability Density Function: S-Orbital
Published: 2013/12/24
Channel: Michel van Biezen
Prob 3 2 Properties of Distribution Function
Prob 3 2 Properties of Distribution Function
Published: 2014/01/19
Channel: Quant Education
Cumulative Distribution Function for C.R.V | دالة التوزيع التراكمية لمتغير عشوائي متصل
Cumulative Distribution Function for C.R.V | دالة التوزيع التراكمية لمتغير عشوائي متصل
Published: 2016/12/27
Channel: jamal505
Geometric distribution cumulative distribution function
Geometric distribution cumulative distribution function
Published: 2016/02/02
Channel: Lawrence Leemis
Bidirectional Reflectance Distribution Function
Bidirectional Reflectance Distribution Function
Published: 2012/09/24
Channel: UCDavis
Distribution Function in R
Distribution Function in R
Published: 2016/08/17
Channel: vivek belhekar
PDF #1 (Deriving Cumulative Distribution Function from Probability Density Function)
PDF #1 (Deriving Cumulative Distribution Function from Probability Density Function)
Published: 2011/01/05
Channel: stepbil
Cumulative Distribution Function for D.R.v|دالة التوزيع التراكمية لمتغير عشوائي منفصل
Cumulative Distribution Function for D.R.v|دالة التوزيع التراكمية لمتغير عشوائي منفصل
Published: 2016/12/24
Channel: jamal505
Cumulative distribution function introduction
Cumulative distribution function introduction
Published: 2012/11/02
Channel: learnittcom
Probability Basics II: The Cumulative Distribution Function (cdf), 2/3/2015
Probability Basics II: The Cumulative Distribution Function (cdf), 2/3/2015
Published: 2015/03/03
Channel: Lutfi Al-Sharif The University of Jordan
Calculating Probabilities Using the Normal Distribution Function in Excel
Calculating Probabilities Using the Normal Distribution Function in Excel
Published: 2015/02/28
Channel: Todd Grande
virtuallymath.com: how to write a cumulative probability distribution function
virtuallymath.com: how to write a cumulative probability distribution function
Published: 2013/06/10
Channel: calculuscoaches
Hydrogen Atom   Radial Probability Distribution for 2s And 3s Orbital
Hydrogen Atom Radial Probability Distribution for 2s And 3s Orbital
Published: 2013/09/01
Channel: Patterns Remonstrator
Atom Electron Orbitals and Radial Distribution Function
Atom Electron Orbitals and Radial Distribution Function
Published: 2015/05/12
Channel: NinetyEast
Lecture 09 - Continuous distribution functions and empirical distribution functions
Lecture 09 - Continuous distribution functions and empirical distribution functions
Published: 2017/07/30
Channel: Modeling and Simulation of Discrete Event Systems
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WIKIPEDIA ARTICLE

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This article describes the distribution function as used in physics. You may be looking for the related mathematical concepts of cumulative distribution function or probability density function.

In molecular kinetic theory in physics, a particle's distribution function is a function of seven variables, , which gives the number of particles per unit volume in single-particle phase space. It is the number of particles per unit volume having approximately the velocity near the place and time . The usual normalization of the distribution function is

where, N is the total number of particles, and n is the number density of particles – the number of particles per unit volume, or the density divided by the mass of individual particles.

A distribution function may be specialised with respect to a particular set of dimensions. E.g. take the quantum mechanical six-dimensional phase space, and multiply by the total space volume, to give the momentum distribution, i.e. the number of particles in the momentum phase space having approximately the momentum .

Particle distribution functions are often used in plasma physics to describe wave–particle interactions and velocity-space instabilities. Distribution functions are also used in fluid mechanics, statistical mechanics and nuclear physics.

The basic distribution function uses the Boltzmann constant and temperature with the number density to modify the normal distribution:

Related distribution functions may allow bulk fluid flow, in which case the velocity origin is shifted, so that the exponent's numerator is , where is the bulk velocity of the fluid. Distribution functions may also feature non-isotropic temperatures, in which each term in the exponent is divided by a different temperature.

Plasma theories such as magnetohydrodynamics may assume the particles to be in thermodynamic equilibrium. In this case, the distribution function is Maxwellian. This distribution function allows fluid flow and different temperatures in the directions parallel to, and perpendicular to, the local magnetic field. More complex distribution functions may also be used, since plasmas are rarely in thermal equilibrium.

The mathematical analog of a distribution is a measure; the time evolution of a measure on a phase space is the topic of study in dynamical systems.

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