To print higher-resolution math symbols, click the Hi-Res Fonts for Printing button on the jsMath control panel.

GE Data Analysis (more info) Consume Data In A Unique Way With Data Visualization. Take A Look Now Visualizing.org

Math Encyclopedia for the | Requests | Forums | find people, Docs | Wiki | Random | Advanced search by the donor list - find out how RSS people. Login multinomial distribution (Definition) create new user Let X = (X1 Xn) be a random vector such that name: 1. Xi 0 and Xi pass: 2. X1 + + Xn = N , where N is a fixed integer login

forget your password? Then X has a multinomial distribution if there exists a parameter vector = ( 1 n) such that Main Menu sections 1. i 0 and i Encyclopædia 2. 1 + + n = 1 Papers 3. has a discrete function in the form: Books X fX(x) Expositions N! f (x) = n xi meta X i=1 i x1! xn! Requests (233) Orphanage Remarks Unclass'd (1) Unproven (567) E[X] = N Corrections (54) Classification Var[X] = (vij) , where

talkback Polls Forums Feedback Bug Reports When n = 2 , the multinomial distribution is the same as the binomial downloads distribution Snapshots If X Xn are mutually independent Poisson random variables with PM Book 1 parameters 1 n respectively, then the conditional joint distribution of 1 information X1 Xn given that X1 + + Xn = N is multinomial with parameters News , where = . Docs i i Wiki ChangeLog Sketch of proof. Each Xi is distributed as: TODO List x Copyright e− i i About f (x ) = i Xi i xi!

The mutual independence of the Xi 's shows that the joint probability distribution of the Xi 's is given by x x e− i i i n i − n i fX(x) = i=1 = e i=1 xi! xi!

where X = (X1 Xn) , x = (x1 xn) and = 1 + + n . Next, let X = X1 + + Xn . Then X is Poisson distributed with parameter (which can be shown by using induction and the mutual independence of the Xi 's): e− x f (x) = X x! The conditional probability distribution of X given that X = N is thus given by:

x f (x) i e− N N! X − n i n i xi fX(x X = N) = = (e i=1 ) ( ) = i=1( ) fX(N) xi! N! x1! xn!

where xi = N and that i = 1 .

"multinomial distribution" is owned by CWoo. (view preamble | get metadata)

View style: jsMath HTML reload

Log in to rate this entry. (view current ratings) Cross-references: conditional probability, induction, distribution, proof, multinomial, joint distribution, conditional, Poisson random variables, independent, , probability distribution function, discrete, vector, parameter, integer, fixed, random vector There are 2 references to this entry.

This is version 4 of multinomial distribution, born on 2004-08-26, modified 2006-10-02. Object id is 6113, canonical name is MultinomialDistribution. Accessed 11722 times total.

Classification: AMS MSC: 60E05 ( and stochastic processes :: Distribution theory :: Distributions: general theory)

Pending Errata and Addenda None. [ View all 2 ] Discussion

Style: Threaded Expand: 1 Order: Newest first reload forum policy

No messages. Interact post | correct | update request | add derivation | add example | add (any)