marginal distribution


Given random variablesMathworldPlanetmath X1,X2,,Xn and a subset I{1,2,,n}, the marginal distribution of the random variables Xi:iI is the following:

f{Xi:iI}(𝐱)={xi:iI}fX1,,Xn(x1,,xn) or
f{Xi:iI}(𝐱)={xi:iI}fX1,,Xn(u1,,un){ui:iI}dui,

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

This is, the marginal distribution of a set of random variables X1,,Xn can be obtained by summing (or integrating) the joint distributionPlanetmathPlanetmath 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).

Title marginal distribution
Canonical name MarginalDistribution
Date of creation 2013-03-22 11:55:00
Last modified on 2013-03-22 11:55:00
Owner mathcam (2727)
Last modified by mathcam (2727)
Numerical id 10
Author mathcam (2727)
Entry type Algorithm
Classification msc 60E05
Synonym marginal density function
Synonym marginal probability function