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The conjugate prior distribution of a categorical distribution is a Dirichlet distribution. [2] See the section below for more discussion. The sufficient statistic from n independent observations is the set of counts (or, equivalently, proportion) of observations in each category, where the total number of trials (=n) is fixed.
The Dirichlet distribution, a generalization of the beta distribution. The Ewens's sampling formula is a probability distribution on the set of all partitions of an integer n, arising in population genetics. The Balding–Nichols model; The multinomial distribution, a generalization of the binomial distribution.
Categorical distribution, for a single categorical outcome (e.g. yes/no/maybe in a survey); a generalization of the Bernoulli distribution; Multinomial distribution, for the number of each type of categorical outcome, given a fixed number of total outcomes; a generalization of the binomial distribution
The Dirichlet distribution is the conjugate prior distribution of the categorical distribution (a generic discrete probability distribution with a given number of possible outcomes) and multinomial distribution (the distribution over observed counts of each possible category in a set of categorically distributed observations).
The categorical distribution is the generalization of the Bernoulli distribution for variables with any constant number of discrete values. The Beta distribution is the conjugate prior of the Bernoulli distribution. [5] The geometric distribution models the number of independent and identical Bernoulli trials needed to get one success.
When k is bigger than 2 and n is 1, it is the categorical distribution. The term "multinoulli" is sometimes used for the categorical distribution to emphasize this four-way relationship (so n determines the suffix, and k the prefix). The Bernoulli distribution models the outcome of a single Bernoulli trial.
The probability distribution associated with a random categorical variable is called a categorical distribution. Categorical data is the statistical data type consisting of categorical variables or of data that has been converted into that form, for example as grouped data .
The Dirichlet distribution is a conjugate distribution to the multinomial distribution. This fact leads to an analytically tractable compound distribution.For a random vector of category counts = (, …,), distributed according to a multinomial distribution, the marginal distribution is obtained by integrating on the distribution for p which can be thought of as a random vector following a ...