For an example, for more specific discussion and for some cautions about certain tricky issues, see the Dirichlet-multinomial distribution article.
22.
The families of multinomial distributions with fixed number of trials " n " but unknown probability parameter ( s ) are exponential families.
23.
The three variants of the categorical distribution and multinomial distribution are due to the fact that the parameters p _ i are constrained, such that
24.
:: I don't see where that L ( n ) came from, shouldn't that just be a multinomial distribution?
25.
The Dirichlet distribution is the conjugate prior for the multinomial distribution, which means that the posterior distribution is also a Dirichlet distribution with different parameters.
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One of the reasons for doing this is that Gibbs sampling of the Dirichlet-multinomial distribution is extremely easy; see that article for more information.
27.
A sum of independent repetitions of this experiment is an observation from a multinomial distribution with " n " equal to the number of such repetitions.
28.
The Negative Multinomial distribution may be used to model the cancer rates at a given site and help measure some of the cancer type dependencies within each location.
29.
However, many problems involve more than the two possible outcomes of a binomial, and instead require 3 or more categories, which leads to the multinomial distribution.
30.
In statistics, the "'multinomial test "'is the test of the null hypothesis that the parameters of a multinomial distribution equal specified values.
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