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Glossary Statistics / Term

Multinomial Distribution

Consider a sequence of n independent trials, each of which can result in an outcome in any of k categories. Let pj be the probability that each trial results in an outcome in category j, j = 1, 2, … , k, so

p1 + p2 + … + pk = 100%.

The number of outcomes of each type has a multinomial distribution. In particular, the probability that the n trials result in n1 outcomes of type 1, n2 outcomes of type 2, … , and nk outcomes of type k is

n!/(n1! × n2! × … × nk!) × p1n1 × p2n2 × … × pknk,

if n1, … , nk are nonnegative integers that sum to n; the chance is zero otherwise.

Permanent link Multinomial Distribution - Creation date 2021-08-07


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