A probability distribution is a measure used in probability theory whose integral over some subspace of a measurable space is regarded as assigning a probability for some event to take values in this subset.
Often a probability density.
A probability distribution is a measure $\rho$ on a measurable space $X$ such that
it is positive: $\forall U \subset X : \int_U d\rho \geq 0$;
it is normalized: $\int_X d\rho = 1$.
In measure theory, a probability measure or probability distribution on a $\sigma$-frame or more generally a $\sigma$-complete distributive lattice $(L, \leq, \bot, \vee, \top, \wedge, \Vee)$ is a probability valuation $\mu:L \to [0, 1]$ such that the elements are mutually disjoint and the probability valuation is denumerably/countably additive
The collection of all probability distributions on a measurable space carries various metric structures that are studied in information geometry:
Last revised on February 7, 2024 at 17:04:32. See the history of this page for a list of all contributions to it.