The Probability Distributome Project is an open-source, open content-development project for exploring, discovering, navigating, learning, and computational utilization of diverse probability distributions. A probability distribution is a function that assigns probabilities to events. For example, flipping a fair coin generates 2 possible equally likely outcomes (head and tail), and rolling a single loaded 6-face die generates 6 possible outcomes, each having a chance to be observed proportionally-equal to the die’s loading factors. Usually, a probability distribution function is defined in the context of a random variable, or a vector, and provides likelihoods that the random variable may be observed within a specific sub-set of the space of its possibilities. For instance, throwing a dart at a dartboard generates a score (integer value), indicating the landing location’s proximity to the center of the dartboard (bulls eye), which naturally leads to a definition of the probability distribution of the dart landing in a specific area.

Probability distributions are mathematically rich objects that give rise to other mathematical functors. Depending on the nature of the space where a probability distribution is defined (discrete, continuous, univariate, multivariate, Euclidian and non-Euclidean, etc.), it naturally leads to various functors like  probability mass or density function, distribution function, quantile function, probability and moment generating functions, and so on. In its most general form, a probability distribution is defined as mapping between a measurable space and the unitary interval.

Distributome Project
The interactive Distributome graphical user Navigator (requires JavaScript-enabled browser) facilitates the traversal, discovery and exploration of the Distributome meta-data, as well as enables the community of users to review, update, expand and submit meta-data revisions to improve this infrastructure. Examples of core Distributome functionality includes:

Dinov, ID, Siegrist, K, Pearl, DK, Kalinin, A, Christou, N (2015). Probability Distributome: a web computational infrastructure for exploring the properties, interrelations, and applications of probability distributions. Computational Statistics, 594: 1-19. DOI: 10.1007/s00180-015-0594-6