Categorical distribution

In probability theory and stat ist ics, a categorical distribut ion (occasionally "discrete distribut ion" or "mult inomial distribut ion", both imprecise usages) is a probability distribut ion that describes the result of a random event that can take on one of K possible outcomes, with the probability of each outcome separately specif ied. There is not necessarily an underlying ordering of these outcomes, but numerical labels are at tached for convenience in describing the distribut ion, of ten in the range 1 to K. Note that the K-dimensional categorical distribut ion is the most general distribut ion over a K-way event; any other discrete distribut ion over a size-K sample space is a special case. The parameters specifying the probabilit ies 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.