Probability Distributions for Directional Data on Smooth Manifolds Wiley Series in Probability and Statistics Series

This book provides a comprehensive and rigorous treatment of real-life scientific problems which encounter non-linear data. The authors first present methods for developing distributions on a circle. Then, they proceed to show how such methods are generalized for other manifolds. They also consider new methods peculiar to certain other manifolds, like disc and hyperdisc. The organization of the book develops the methods from the beginning for a simple manifold, letting the reader appreciate how these unfold and generalize to more complicated manifolds. Next, rather than separately treating one distribution at a time, the authors develop the generalizations of the methods of derivations. Finally, new distributions are presented as outcomes of these generalizations. The authors also provide several real-life examples, which not only attest to the ongoing usefulness, but will also help the reader visualize other modern day areas of the applications of these important distributions.

Ashis SenGupta, PhD, is Professor in the Applied Statistics Unit at Indian Statistical Institute, Kolkata, India. He received his PhD in Statistics from Ohio State University, USA. Dr. SenGupta is also Adjunct Professor in the Department of Biostatistics and Epidemiology at Augusta University, Georgia, USA. He is a Life Member of the International Indian Statistical Association and the International Forum for Interdisciplinary Mathematics.

Kunio Shimizu, PhD, is Adjunct Professor in the School of Statistical Thinking at The Institute of Statistical Mathematics, Tokyo, Japan. He is also Professor Emeritus in the Faculty of Science and Technology at Keio University, Tokyo, Japan. Dr. Shimizu is currently the Chair of the Working Group on Mathematical Statistics at the Science Council of Japan. In 2001 he was awarded the Jacob Wolfowitz Prize by the American Journal of Mathematical and Management Sciences.