Multinomial distribution
Probability distribution, Statistical independence, Bernoulli trial, Categorical distribution, Integer, Probability mass function, Variance
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In probability theory, the multinomial distribution is a generalization of the binomial distribution. The binomial distribution is the probability distribution of the number of "successes" in n independent Bernoulli trials, with the same probability of "success" on each trial. In a multinomial distribution, the analog of the Bernoulli distribution is the categorical distribution, where each trial results in exactly one of some fixed finite number k of possible outcomes, with probabilities p1, ..., pk (so that pi ¿ 0 for i = 1, ..., k and sum_{i=1}^k p_i = 1), and there are n independent trials. Then let the random variables Xi indicate the number of times outcome number i was observed over the n trials. The vector X = (X1, ..., Xk) follows a multinomial distribution with parameters n and p, where p = (p1, ..., pk).
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