Probability Distributions for Directional Data on Smooth Manifolds

A text that focuses on methods of deriving probability distributions on smooth manifolds popular in applied research

Probability Distributions for Directional Data on Smooth Manifolds is a comprehensive text that reviews real-life scientific problems that encounter non-linear data. The authors—noted experts on the topic—present methods for developing distributions on a circle and show how such methods are generalized for other manifolds. In addition, the book explores new methods unique to other manifolds such as disc and hyperdisc.

Designed to be an accessible resource, the book explores the methods from the beginning for a simple manifold and clearly demonstrates how these unfold and generalize to more complicated manifolds. Rather than treating one distribution at a time, the authors develop the generalizations of the methods of derivations. As the outcomes of these generalizations are reviewed, new distributions are presented. In addition, the book provides several illustrative, real-life examples, which not only attest to the ongoing usefulness of these important distributions but can help visualize other modern-day areas of the applications. This important resource:

• Offers a compilation of the probability distributions of the various manifolds presented
• Covers many emerging distributions and topics which have not been covered in any book to date
• Presents discussions on axial distributions, distributions on the sphere, hemi-sphere and hyper-sphere, and distributions on the (ring) torus and hyper-torus
• Contains information on distributions on the (vertical) cylinder and hyper-cylinder, distributions on the disc and hyper-disc, isotropy and goodness of fit tests, and mathematical formulae

Written for students of mathematics and statistics and theoretical researchers, Probability Distributions for Directional Data on Smooth Manifolds, the first of its kind, offers a groundbreaking and authoritative guide to the topic.