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,…, nm≤n and with . The random variable Xj has expectation npj and variance npj(1−pj) and the covariance of Xj and Xk (j≠k) is−npjpk. The term ‘multinomial distribution’ was introduced by Sir Ronald Fisher in 1925.
Subjects: Probability and Statistics.