Categorical distribution

In probability theory and statistics, a categorical distribution (also called a "generalized Bernoulli distribution", "multinoulli distribution" or, less precisely, a "discrete distribution") is a probability distribution that describes the possible results of a random event that can take on one of K possible outcomes, with the probability of each outcome separately specified. There is not necessarily an underlying ordering of these outcomes, but numerical labels are often attached for convenience in describing the distribution, (e.g. 1 to K). Note that 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.