PlanetMath (more info)
 Math for the people, by the people.
Encyclopedia | Requests | Forums | Docs | Wiki | Random | RSS  
Login
create new user
name:
pass:
forget your password?
Main Menu
sections
Encyclopædia
Papers
Books
Expositions

meta
Requests (204)
Orphanage
Unclass'd
Unproven (490)
Corrections (7)
Classification

talkback
Polls
Forums
Feedback
Bug Reports

downloads
Snapshots
PM Book

information
News
Docs
Wiki
ChangeLog
TODO List
Legalese
About
Owner confidence rating: High Entry average rating: No information on entry rating
marginal distribution (Algorithm)

Given random variables $ X_1, X_2, ... , X_n$ and a subset $ I \subset \{1,2,...,n\}$, the marginal distribution of the random variables $ {X_i : i \in I}$ is the following:

$ f_{\{X_i : i \in I\}}(\mathbf{x}) = \sum_{\{x_i : i \notin I\}}^{}{ f_{X_1,...,X_n}(x_1,...,x_n) }$ or
$ f_{\{X_i : i \in I\}}(\mathbf{x}) = \int_{\{x_i : i \notin I\}}^{}{ f_{X_1,...,X_n}(u_1,...,u_n) \prod_{ \{u_i : i \notin I\} }^{} du_i}$,

summing if the variables are discrete and integrating if the variables are continuous.

This is, the marginal distribution of a set of random variables $ X_1,...,X_n$ can be obtained by summing (or integrating) the joint distribution over all values of the other variables.

The most common marginal distribution is the individual marginal distribution (ie, the marginal distribution of ONE random variable).



"marginal distribution" is owned by mathcam. [ full author list (2) | owner history (1) ]
(view preamble)

View style:

Other names:  marginal density function, marginal probability function
Log in to rate this entry.
(view current ratings)

Cross-references: joint distribution, continuous, discrete, variables, summing, subset, random variables
There is 1 reference to this entry.

This is version 5 of marginal distribution, born on 2001-10-26, modified 2004-06-09.
Object id is 591, canonical name is MarginalDistribution.
Accessed 21449 times total.

Classification:
AMS MSC: 60E05 (Probability theory and stochastic processes :: Distribution theory :: Distributions: general theory)
Pending Errata and Addenda
None.
[ View all 2 ]
Discussion
Style: Expand: Order:
forum policy

No messages.

Interact
post | correct | update request | add example | add (any)