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Cumulative Distribution Function - Probability
Cumulative Distribution Function - Probability
Published: 2012/02/11
Channel: Engineer Clearly
Probability density functions | Probability and Statistics | Khan Academy
Probability density functions | Probability and Statistics | Khan Academy
Published: 2009/02/16
Channel: Khan Academy
The Probability Distribution Function (PDF) of [X]
The Probability Distribution Function (PDF) of [X]
Published: 2014/02/26
Channel: MIT OpenCourseWare
Calculating a Cumulative Distribution Function (CDF)
Calculating a Cumulative Distribution Function (CDF)
Published: 2014/02/26
Channel: MIT OpenCourseWare
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
Probability Mass Function & Density Function in Hindi
Probability Mass Function & Density Function in Hindi
Published: 2015/05/15
Channel: Bhagwan Singh Vishwakarma
probability density functions and cumulative distribution functions s1
probability density functions and cumulative distribution functions s1
Published: 2013/02/14
Channel: Rhys Steele
Probability Density Functions / Continuous Random Variables
Probability Density Functions / Continuous Random Variables
Published: 2009/06/26
Channel: patrickJMT
PDF and CDF Explanations
PDF and CDF Explanations
Published: 2011/04/21
Channel: UAMath115
Probability : Cumulative Distribution Function F(X) : ExamSolutions
Probability : Cumulative Distribution Function F(X) : ExamSolutions
Published: 2011/04/14
Channel: ExamSolutions
Orbitals: Nodes and Radial Distribution Function
Orbitals: Nodes and Radial Distribution Function
Published: 2017/02/25
Channel: Chemistry_OK OSU
Continuous Random Variables: Cumulative Distribution Functions
Continuous Random Variables: Cumulative Distribution Functions
Published: 2012/11/27
Channel: MrNichollTV
Finding a CDF from a pdf
Finding a CDF from a pdf
Published: 2015/11/26
Channel: Mr Camilleri
Method of Distribution Functions 1
Method of Distribution Functions 1
Published: 2014/11/03
Channel: Matthew Jones
Cumulative Distribution Function
Cumulative Distribution Function
Published: 2012/06/13
Channel: David Waldo
Continuous Random Variables: Probability Density Functions
Continuous Random Variables: Probability Density Functions
Published: 2014/01/28
Channel: MrNichollTV
Lecture - 5 Probability Distributions and Density Functions
Lecture - 5 Probability Distributions and Density Functions
Published: 2008/07/10
Channel: nptelhrd
Cumulative Distribution Function : Example : ExamSolutions
Cumulative Distribution Function : Example : ExamSolutions
Published: 2009/12/05
Channel: ExamSolutions
Cumulative Distribution Functions : Introduction : ExamSolutions
Cumulative Distribution Functions : Introduction : ExamSolutions
Published: 2009/12/04
Channel: ExamSolutions
Mod-01 Lec-16 CUMULATIVE DISTRIBUTION FUNCTION
Mod-01 Lec-16 CUMULATIVE DISTRIBUTION FUNCTION
Published: 2015/02/19
Channel: nptelhrd
Section 5 1 Distribution Function Technique
Section 5 1 Distribution Function Technique
Published: 2017/04/19
Channel: Karen Benway
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
Discrete Random Variables 2)   Cumulative Distribution Function
Discrete Random Variables 2) Cumulative Distribution Function
Published: 2013/08/26
Channel: ukmathsteacher
An Introduction to the Normal Distribution
An Introduction to the Normal Distribution
Published: 2012/12/23
Channel: jbstatistics
Prob 3 2 Properties of Distribution Function
Prob 3 2 Properties of Distribution Function
Published: 2014/01/19
Channel: Quant Education
Python tutorial: Cumulative Distribution Functions
Python tutorial: Cumulative Distribution Functions
Published: 2016/11/09
Channel: DataCamp
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
An Introduction to Continuous Probability Distributions
An Introduction to Continuous Probability Distributions
Published: 2012/12/23
Channel: jbstatistics
Introduction to discrete probability distributions
Introduction to discrete probability distributions
Published: 2012/12/07
Channel: Khan Academy
Gaussian
Gaussian
Published: 2012/12/12
Channel: Paul Francis
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
Marginal distribution and conditional distribution
Marginal distribution and conditional distribution
Published: 2016/11/16
Channel: Khan Academy
Normal distribution
Normal distribution's probability density function derived in 5min
Published: 2013/08/22
Channel: acadelivery
FRM: Normal probability distribution
FRM: Normal probability distribution
Published: 2008/01/15
Channel: Bionic Turtle
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
Exponential distribution cumulative distribution function
Exponential distribution cumulative distribution function
Published: 2016/02/16
Channel: Lawrence Leemis
Electronic Devices: Fermi Dirac distribution
Electronic Devices: Fermi Dirac distribution
Published: 2015/05/04
Channel: techgurukula
The Binomial Distribution / Binomial Probability Function
The Binomial Distribution / Binomial Probability Function
Published: 2009/05/06
Channel: patrickJMT
Joint Probability Distribution # 1 | Marginal Distributions & Expected Values
Joint Probability Distribution # 1 | Marginal Distributions & Expected Values
Published: 2015/02/24
Channel: WelshBeastMaths
Probability Mass Function
Probability Mass Function
Published: 2012/02/11
Channel: Engineer Clearly
Cumulative distribution function introduction
Cumulative distribution function introduction
Published: 2012/11/02
Channel: learnittcom
An Introduction to the Continuous Uniform Distribution
An Introduction to the Continuous Uniform Distribution
Published: 2012/12/28
Channel: jbstatistics
39- Joint CDF
39- Joint CDF
Published: 2015/03/26
Channel: Probability Course
Continuous probability distribution intro
Continuous probability distribution intro
Published: 2012/12/10
Channel: Khan Academy
Finding Probabilities and Percentiles for a Continuous Probability Distribution
Finding Probabilities and Percentiles for a Continuous Probability Distribution
Published: 2012/12/28
Channel: jbstatistics
Multivariate distributions:  joint cumulative distribution functions -- Example 1
Multivariate distributions: joint cumulative distribution functions -- Example 1
Published: 2016/03/09
Channel: Lawrence Leemis
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
Cumulative Distribution Function of an Order Statistic
Cumulative Distribution Function of an Order Statistic
Published: 2014/10/06
Channel: Ben Garside
How to Construct a Cumulative Distribution Plot in Excel 2007
How to Construct a Cumulative Distribution Plot in Excel 2007
Published: 2011/10/18
Channel: Dr. Cyders
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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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