title: Probability Distributome: A Web Computational Infrastructure for Exploring the Properties, Interrelations, and Applications of Probability Distributions.
abstract: Probability distributions are useful for modeling, simulation, analysis, and inference on varieties of natural processes and physical phenomena. There are uncountably many probability distributions. However, a few dozen families of distributions are commonly defined and are frequently used in practice for problem solving, experimental applications, and theoretical studies. In this paper, we present a new computational and graphical infrastructure, theDistributome, which facilitates the discovery, exploration and application of diverse spectra of probability distributions. The extensible Distributome infrastructure provides interfaces for (human and machine) traversal, search, and navigation of all common probability distributions. It also enables distribution modeling, applications, investigation of inter-distribution relations, as well as their analytical representations and computational utilization. The entire Distributome framework is designed and implemented as an open-source, community-built, and Internet-accessible infrastructure. It is portable, extensible and compatible with HTML5 and Web2.0 standards (http://Distributome.org). We demonstrate two types of applications of the probability Distributome resources: computational research and science education. The Distributome tools may be employed to address five complementary computational modeling applications (simulation, data-analysis and inference, model-fitting, examination of the analytical, mathematical and computational properties of specific probability distributions, and exploration of the inter-distributional relations). Many high school and college science, technology, engineering and mathematics (STEM) courses may be enriched by the use of modern pedagogical approaches and technology-enhanced methods. The Distributome resources provide enhancements for blended STEM education by improving student motivation, augmenting the classical curriculum with interactive webapps, and overhauling the learning assessment protocols.
authors.affiliation: Statistics Online Computational Resource (SOCR), Michigan Institute for Data Science (MIDAS), School of Nursing, University of Michigan, Ann Arbor, MI 48109; SOCR Resource, Department of Statistics, University of California, Los Angeles, Los Angeles, CA 90095; Center for Computational Biology, University of California, Los Angeles, Los Angeles, CA 90095.
authors.forename: Ivo D
authors.initials: ID
authors.lastname: Dinov
authors.affiliation: Department of Mathematical Sciences, University of Alabama, Huntsville, AL 35899.
authors.forename: Kyle
authors.initials: K
authors.lastname: Siegrist
authors.affiliation: Department of Statistics, Pennsylvania State University, State College, PA 16801.
authors.forename: Dennis K
authors.initials: DK
authors.lastname: Pearl
authors.affiliation: Statistics Online Computational Resource (SOCR), Michigan Institute for Data Science (MIDAS), School of Nursing, University of Michigan, Ann Arbor, MI 48109.
authors.forename: Alexandr
authors.initials: A
authors.lastname: Kalinin
authors.affiliation: SOCR Resource, Department of Statistics, University of California, Los Angeles, Los Angeles, CA 90095.
authors.forename: Nicolas
authors.initials: N
authors.lastname: Christou
keywords: Distributome; Probability distributions; applications; graphical user interface; inference; models; transformations