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When k = 2, the multinomial distribution is the binomial distribution. Categorical distribution, the distribution of each trial; for k = 2, this is the Bernoulli distribution. The Dirichlet distribution is the conjugate prior of the multinomial in Bayesian statistics. Dirichlet-multinomial distribution. Beta-binomial 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. The multivariate normal distribution, a generalization of the normal distribution.
In probability theory and statistics, the negative multinomial distribution is a generalization of the negative binomial distribution (NB(x 0, p)) to more than two outcomes. [ 1 ] As with the univariate negative binomial distribution, if the parameter x 0 {\displaystyle x_{0}} is a positive integer, the negative multinomial distribution has an ...
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 ...
The Dirichlet distribution is a conjugate distribution to the negative multinomial distribution. This fact leads to an analytically tractable compound distribution.For a random vector of category counts = (, …,), distributed according to a negative multinomial distribution, the compound distribution is obtained by integrating on the distribution for p which can be thought of as a random ...
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 ...
The equidensity contours of a non-singular multivariate normal distribution are ellipsoids (i.e. affine transformations of hyperspheres) centered at the mean. [29] Hence the multivariate normal distribution is an example of the class of elliptical distributions.
Multinomial logistic regression is known by a variety of other names, including polytomous LR, [2] [3] multiclass LR, softmax regression, multinomial logit (mlogit), the maximum entropy (MaxEnt) classifier, and the conditional maximum entropy model.