Bibliog. data: 1st ed. 2022. 2022. iv, 846 S. IV, 846 p. 3 illus. 235 mm
ISBN-13: 9783030958633
This book explores topics in multivariate statistical analysis, relevant in real and complex domains. It utilizes simplified and unified notations to render the complex subject matter both accessible and enjoyable, drawing from clear exposition and numerous illustrative examples. The book features an in-depth treatment of theory with a fair balance of applied coverage, and a classroom lecture style so that the learning process feels organic. It also features original results, with the goal of driving research conversations forward. This will be particularly useful for researchers working in machine learning, biomedical signal processing, and other fields that increasingly rely on complex random variables to model complex-valued data. It can also be used in advanced courses on multivariate analysis. Additional exercises are provided.
1. Mathematical Preliminaries.- 2. The Univariate Gaussian and Related Distribution.- 3. Multivariate Gaussian and Related Distributions.- 4. The Matrix-variate Gaussian Distribution.- 5. Matrix-variate Gamma and Beta Distributions.- 6. Hypothesis Testing and Null Distributions.- 7. Rectangular Matrix-variate Distributions.- 8. Distributions of Eigenvalues and Eigenvectors.- 9. Principal Component Analysis.- 10. Canonical Correlation Analysis.- 11. Factor Analysis.- 12. Classification Problems.- 13. Multivariate Analysis of Variance (MANOVA).- 14. Profile Analysis and Growth Curves.- 15. Cluster Analysis and Correspondence Analysis.
Dr. A.M. Mathai is professor emeritus at McGill University and visiting professor at many other universities around the world. He has published over 37 books and over 300 research articles. Dr. Mathai has been invited to speak at conferences, universities, and other institutes around the world. His areas of research include applied statistics, probability, and mathematical statistics. Dr. Serge B. Provost is professor at the University of Western Ontario. His research interests include multivariate analysis, computational statistics and distribution theory, with applications involving problems arising in various areas of scientific investigations such as biostatistics, finance, optics, imaging, and machine learning. Dr. Provost has received three teaching awards and chaired a national fellowship and scholarship selection committee. He is a fellow and chartered statistician of the Royal Statistical Society. Dr. Hans J. Haubold is professor of t
Theoretical astrophysics at the Office for Outer Space Affairs of the United
Nations. His research interest focuses on the internal structure of the
sun, solar neutrinos, and special functions of mathematical physics. He
is also interested in the history of astronomy, physics, and mathematics,
specifically Einstein"s and Michelson"s contributions to theoretical
and experimental physics. Dr. Haubold is a member of the American Astronomical
Society, the American Mathematical Society, and the History of Science
Society.
Format: Paperback / softback,
106 pages, height x width: 235x155 mm,
6 Illustrations, black and white; VIII, 106 p. 6 illus.
Series: JSS Research Series in Statistics
Pub. Date: 19-May-2022
ISBN-13: 9789811910722
This book presents new computation schemes for the sensitivity of options using the binomial tree and introduces readers to the discrete Malliavin calculus. It also shows that applications of the discrete Malliavin calculus approach to the binomial tree model offer fundamental tools for computing Greeks.
The binomial tree approach is one of the most popular methods in option pricing. Although it is a fairly traditional model for option pricing, it is still widely used in financial institutions since it is tractable and easy to understand. However, the book shows that the tree approach also offers a powerful tool for deriving the Greeks for options. Greeks are quantities that represent the sensitivities of the price of derivative securities with respect to changes in the underlying asset price or parameters.
The Malliavin calculus, the stochastic methods of variations, is one of the most popular tools used to derive Greeks. However, it is also very difficult to understand for most students and practitioners because it is based on complex mathematics. To help readers more easily understand the Malliavin calculus, the book introduces the discrete Malliavin calculus, a theory of the functional for the Bernoulli random walk. The discrete Malliavin calculus is significantly easier to understand, because the functional space of the Bernoulli random walk is realized in a finite dimensional space. As such, it makes this valuable tool far more accessible for a broad readership.
Introduction.- Single-Period Model.- Multiple Time Model.- Application to Finance.- Spectral Binomial Tree.- Short Introduction to Malliavin Calculus in Continuous Time Model.- Discrete Malliavin Greeks.
Format: Paperback / softback,
56 pages, height x width: 235x155 mm, X, 56 p.
Series: SpringerBriefs in Mathematics
Pub. Date: 29-May-2022
ISBN-13: 9789811912382
The focus of this book is on the further development of the classical achievements in analysis of several complex variables, the analytic continuation and the analytic structure of sets, to settings in which the q-pseudoconvexity in the sense of Rothstein and the q-convexity in the sense of Grauert play a crucial role. After giving a brief survey of notions of generalized convexity and their most important results, the authors present recent statements on analytic continuation related to them.
Rothstein (1955) first introduced q-pseudoconvexity using generalized Hartogs figures. Slodkowski (1986) defined q-pseudoconvex sets by means of the existence of exhaustion functions which are q-plurisubharmonic in the sense of Hunt and Murray (1978). Examples of q-pseudoconvex sets appear as complements of analytic sets. Here, the relation of the analytic structure of graphs of continuous surfaces whose complements are q-pseudoconvex is investigated. As an outcome, the authors generalize results by Hartogs (1909), Shcherbina (1993), and Chirka (2001) on the existence of foliations of pseudoconcave continuous real hypersurfaces by smooth complex ones.
A similar generalization is obtained by a completely different approach using L2-methods in the setting of q-convex spaces. The notion of q-convexity was developed by Rothstein (1955) and Grauert (1959) and extended to q-convex spaces by Andreotti and Grauert (1962). Andreotti?Grauert's finiteness theorem was applied by Andreotti and Norguet (1966?1971) to extend Grauert's solution of the Levi problem to q-convex spaces. A consequence is that the sets of (q-1)-cycles of q-convex domains with smooth boundaries in projective algebraic manifolds, which are equipped with complex structures as open subsets of Chow varieties, are in fact holomorphically convex. Complements of analytic curves are studied, and the relation of q-convexity and cycle spaces is explained. Finally, results for q-convex domains in projective spaces are shown and the q-convexity in analytic families is investigated.
1. Analytic Continuation and Pseudoconvexity.-
2. q-Plurisubharmonicity.-
3. q-Pseudoconvexity.-
4. q-Convexity and q-Completeness.- References.- Index.
Format: Hardback,
479 pages, height x width: 235x155 mm,
93 Illustrations, color; 44 Illustrations, black and white; XIV, 479 p. 137 illus., 93 illus. in color.
Series: Forum for Interdisciplinary Mathematics
Pub. Date: 10-Jun-2022
ISBN-13: 9789811910432
In commemoration of the bicentennial of the birth of the glady who gave the rose diagram to ush, this special contributed book pays a statistical tribute to Florence Nightingale. This book presents recent phenomenal developments, both in rigorous theory as well as in emerging methods, for applications in directional statistics, in 25 chapters with contributions from 65 renowned researchers from 25 countries. With the advent of modern techniques in statistical paradigms and statistical machine learning, directional statistics has become an indispensable tool. Ranging from data on circles to that on the spheres, tori and cylinders, this book includes solutions to problems on exploratory data analysis, probability distributions on manifolds, maximum entropy, directional regression analysis, spatio-directional time series, optimal inference, simulation, statistical machine learning with big data, and more, with their innovative applications to emerging real-life problems in astro-statistics, bioinformatics, crystallography, optimal transport, statistical process control, and so on.
Philippa M. Burdett, Kanti V. Mardia, Stuart Barber, John T. Kent and Thomas Hamelryck: Mixture Models for Spherical Data with Applications to Protein Bioinformatics.-Richard Arnold, Peter Jupp and Helmut Schaeben: Statistics of Orientation Relationships in Crystallography.- S. Rao Jammalamadaka, Gyorgy Terdik and Brian Wainwright: Simulation and Visualization of Spherical Distributions.- Jan Beran, Britta Steffens and Sucharita Ghosh: Some Applications of Long-range Dependence in Directional Data.- Barry C. Arnold and and Ashis SenGupta: Multivariate Power Cardioid Distributions on Hyper-Torus.- Peter Guttorp and Richard Lockhart: GLM Type Regression for Directional Data.- Andriette Bekker, Najmeh Nakhaei Rad, M. Arashi, Christophe Ley: Generalized Skew-Symmetric Circular and Toroidal Distributions.- Riccardo Gatto: Bimodal Spectra and the Generalised von Mises Distribution.- Kunio Shimizu and Tomoaki Imoto: Circular Distribution Constructed from the Product of Cardioid-type Densities with (Hyper-) Toroidal Extension.- Toshihiro Abe, Tomoaki Imoto, Yoichi Miyat, Takayuki Shiohama: Recent Cylindrical Models and their Applications.- Xiaoping Zhan and Tiefeng Ma: A Complex Multiplication Regression Model for Circular Data.- Yogendra P. Chaubey: Nonparametric Density Estimation for Circular Data.- Fred Lombard, Douglas M. Hawkins and Cornelis J. Potgieter: SPC on a Circle: A Review and Some New Results.- S.H. Ong: Bivariate Cardioid Distributions.- Arnab K. Laha and Sourav Majumdar: Angular-Angular and Linear-Angular Regression Using ANN.- Hemangi V. Kulkarni: Efficient Estimation of Concentration Parameter of von Mises Distribution.- Shreyashi Basak, Kanika and Somesh Kumar: Robustness and Efficiency of Estimators for Mean Direction of a Wrapped Cauchy Distribution.- Sungsu Kim and Abeku A. Asare-Kumi: Diagnostic Analysis and Asymptotic Simultaneous Inference of the Three-Parameter Generalized von Mises Distribution.- Atanu Biswas and Jayant Jha: Regression Models for Directional Data.- S.P. Mukherjee: Quality of Life: Florence Nightingale's Call for Improvement.- Francesco Lagona: Spatial Autoregressive Models for Circular Data.- Fidelis Ugwuowo: Models of Directional Time Series with Applications.- Kasirga Yildirak and Serdar Tugac: Wind Speed and Wind Direction Prediction by Deep Learning.- Malay Ghosh: Revisiting Wrapped Cauchy Distribution.- Axel Munk: To Receive.
Format: Hardback,
506 pages, height x width: 235x155 mm,
94 Illustrations, color; 10 Illustrations, black and white; XII, 506 p. 104 illus., 94 illus. in color
Pub. Date: 05-Jun-2022
ISBN-13: 9783030976781
This book discusses diverse concepts and notions ? and their applications ? concerning probability and random variables at the intermediate to advanced level. It explains basic concepts and results in a clearer and more complete manner than the extant literature. In addition to a range of concepts and notions concerning probability and random variables, the coverage includes a number of key advanced concepts in mathematics. Readers will also find unique results on e.g. the explicit general formula of joint moments and the expected values of nonlinear functions for normal random vectors. In addition, interesting applications of the step and impulse functions in discussions on random vectors are presented. Thanks to a wealth of examples and a total of 330 practice problems of varying difficulty, readers will have the opportunity to significantly expand their knowledge and skills. The book is rounded out by an extensive index, allowing readers to quickly and easily find what they are looking for.
Given its scope, the book will appeal to all readers with a basic grasp of probability and random variables who are looking to go one step further. It also offers a valuable reference guide for experienced scholars and professionals, helping them review and refine their expertise.
Preface.
Chapter 1 - Preliminaries.
Chapter 2 - Fundamentals of Probability.
Chapter 3 - Random Variables.
Chapter 4 - Random Vectors.-
Chapter 5 - Normal Random Vectors.
Chapter 6 - Convergence of Random Variables.- Answers to Selected Exercises.- Index.
Format: Hardback,
216 pages, height x width: 235x155 mm, 10 Tables,
color; 12 Illustrations, color; 43 Illustrations, black and white; IV, 216 p. 55 illus., 12 illus. in color
Series: Annals of the Canadian Society for History and Philosophy of Mathematics/ Societe canadienne d'histoire et de philosophie des mathematiques
Pub. Date: 29-May-2022
ISBN-13: 9783030952006
This volume contains eleven papers that have been collected by the Canadian Society for History and Philosophy of Mathematics/Societe canadienne dfhistoire et de philosophie des mathematiques. It showcases rigorously-reviewed contemporary scholarship on an interesting variety of topics in the history and philosophy of mathematics, as well as the teaching of the history of mathematics. Topics considered include
The mathematics and astronomy in Nathaniel Torperlyfs only published work, Diclides Coelometricae, seu valvae astronomicae universal
Connections between the work of Urbain Le Verrier, Carl Gustav Jacob Jacobi, and Augustin-Louis Cauchy on the algebraic eigenvalue problem
An evaluation of Ken Mandersf argument against conceiving of the diagrams in Euclidfs Elements in semantic terms
The development of undergraduate modern algebra courses in the United States
Ways of using the history of mathematics to teach the foundations of mathematical analysis
Written by leading scholars in the field, these papers are accessible not only to mathematicians and students of the history and philosophy of mathematics, but also to anyone with a general interest in mathematics.
J. S. Silverberg, The Most Obscure and Inconvenient Tables ever Constructed.- D. J. Melville, Commercializing Arithmetic: The Case of Edward Hatton.- C. Baltus, Leading to Poncelet: A Story of Collinear Points.- R. Godard, Cauchy, Le Verrier et Jacobi sur le probleme algebrique des valeurs propres et les inegalites seculaires des mouvements des planetes.- A. Ackerberg-Hastings, Mathematics in Astronomy at Harvard College Before 1839 as a Case Study for Teaching Historical Writing in Mathematics Courses.- J. J. Tattersall, S. L. McMurran, "Lectures for Women" and the Founding of Newnham College, Cambridge.- D. Waszek, Are Euclid's Diagrams "Representations"? On an Argument by Ken Manders.- B. Buldt, Abstraction by Embedding and Constraint-Based Design.- W. Meyer, The Birth of Undergraduate Modern Algebra in the United States.- P. Liu, History as a Source of Mathematical Narrative in Developing Students' Interpretations of Mathematics.- F. Kamareddine, J. P. Seldin, Thoughts on Using the History of Mathematics to Teach the Foundations of Mathematical Analysis.