multinomial distribution

Show Summary Details

Quick Reference

The extension of the binomial distribution to the case of more than two classes. For example, suppose that the probabilities of classes 1, 2,…, m are p1, p2,…, pm with . Let Xj denote the number, in a sample of size n, that are in class j, for j=1, 2,…, m. The random variables X1, X2,…, Xm have a multivariate distribution given by , where 0≤n1, n2,…, nmn and with . The random variable Xj has expectation npj and variance npj(1−pj) and the covariance of Xj and Xk (jk) is−npjpk. The term ‘multinomial distribution’ was introduced by Sir Ronald Fisher in 1925.

Subjects: Probability and Statistics.

Reference entries

Users without a subscription are not able to see the full content. Please, subscribe or login to access all content.