A pioneering monograph on tensor methods applied to distributional problems arising in statistics, this work begins with the study of multivariate moments and cumulants. An invaluable reference for graduate students and professional statisticians, it requires some knowledge of linear algebra, eigenvalue decompositions, linear models, and, for later chapters, likelihood functions and likelihood ratio statistics. More than 200 exercises throughout the book are an integral part of the text. AUTHOR: Peter McCullagh studied at The University of Birmingham and received his Ph.D. from Imperial College, London. He is the John D. MacArthur Distinguished Service Professor in the Department of Statistics and the College at The University of Chicago. He is also the co-author (with John Nelder) of Generalized Linear Models (Chapman and Hall, 1983, second edition 1989) which received the inaugural Karl Pearson Prize from the International Statistics Institute. He is a member of The Royal Society (UK) and The American Academy of Arts and Sciences.