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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.