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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 uniform distribution or rectangular distribution on [a,b], where all points in a finite interval are equally likely, is a special case of the four-parameter Beta distribution. The Irwin–Hall distribution is the distribution of the sum of n independent random variables, each of which having the uniform distribution on [0,1].
Categorical distribution This page was last edited on 9 April 2024, at 13:03 (UTC). Text is available under the Creative Commons Attribution-ShareAlike 4.0 License ...
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.
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 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.
It is a multivariate generalization of the beta distribution, [1] hence its alternative name of multivariate beta distribution (MBD). [2] Dirichlet distributions are commonly used as prior distributions in Bayesian statistics, and in fact, the Dirichlet distribution is the conjugate prior of the categorical distribution and multinomial ...
For example, count data requires a different distribution (e.g. a Poisson distribution or binomial distribution) than non-negative real-valued data require, but both fall under the same level of measurement (a ratio scale). Various attempts have been made to produce a taxonomy of levels of measurement.