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Categorical distribution

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In probability theory and statistics, a categorical distribution (also called a generalized Bernoulli distribution, multinoulli distribution) is a discrete probability distribution that describes the possible results of a random variable that can take on one of K possible categories, with the probability of each category separately specified. There is no innate underlying ordering of these outcomes, but numerical labels are often attached for convenience in describing the distribution, (e.g. 1 to K). The K-dimensional categorical distribution is the most general distribution over a K-way event; any other discrete distribution over a size-K sample space is a special case. The parameters specifying the probabilities of each possible outcome are constrained only by the fact that each must be in the range 0 to 1, and all must sum to 1.

Categorical distribution - Wikipedia Jump to content From Wikipedia, the free encyclopedia Discrete probability distribution k > 0</math> number of categories ([[integer]])<br /><math>p_1, \\ldots, p_k</math> event probabilities <math>(p_i \\geq 0,\\,\\Sigma p_i = 1)</math>"},"support":{"wt":"<math>x \\in \\{1,\\dots,k\\}</math>"},"pdf":{"wt":"(1) <math>p(x=i)=p_i</math><br />\n(2) <math>p(x) = p_1^{[x=1]} \\cdots p_k^{[x=k]}</math><br />\n{{nowrap|(3) <math>p(x) = [x=1]\\cdot p_1 \\, + \\cdots + \\, [x=k]\\cdot p_k</math>}}\n: where <math>[x=i]</math> is the [[Iverson bracket]]"},"mode":{"wt"

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