This major revision contains a largely new chapter 7 providing an extensive discussion of the bivariate and multivariate versions of the standard distributions and families. Chapter 16 has been enlarged to cover multivariate sampling theory, an updated version of material previously found inthe old Volume III. The previous chapters 7 and 8 have been condensed into a single chapter providing an introduction to statistical inference. Elsewhere, major updates include new material on skewness and kurtosis, hazard rate distributions, the bootstrap, the evaluation of the multivariate normalintegral and ratios of quadratic forms. The new edition includes over 200 new references, 40 new exercises and 20 further examples in the main text. In addition, all the text examples have been given titles, and these are listed at the front of the book for easier reference.

This 3-volume set offers the complete, classic Kendall's Advanced Theory of Statistics in a single, value-for-money pack. The latest set includes the brand new second edition of the popular 'Volume 2B: Bayesian Inference', along with the sixth editions of 'Volume 1: Distribution Theory' and 'Volume 2A: Classical Inference and the Linear Model'.

Shape and Shape Theory D. G. Kendall Churchill College, University of Cambridge, UK D. Barden Girton College, University of Cambridge, UK T. K. Carne King's College, University of Cambridge, UK H. Le University of Nottingham, UK The statistical theory of shape is a relatively new topic and is generating a great deal of interest and comment by statisticians, engineers and computer scientists. Mathematically, 'shape' is the geometrical information required to describe an object when location, scale and rotational effects are removed. The theory was pioneered by Professor David Kendall to solve practical problems concerning shape. This text presents an elegant account of the theory of shape that has evolved from Kendall's work. Features include: * A comprehensive account of Kendall's shape spaces * A variety of topological and geometric invariants of these spaces * Emphasis on the mathematical aspects of shape analysis * Coverage of the mathematical issues for a wide range of applications The early chapters provide all the necessary background information, including the history and applications of shape theory. The authors then go on to analyse the topic, in brilliant detail, in a variety of different shape spaces. Kendall's own procedures for visualising distributions of shapes and shape processes are covered at length. Implications from other branches of mathematics are explored, along with more advanced applications, incorporating statistics and stochastic analysis. Applied statisticians, applied mathematicians, engineers and computer scientists working and researching in the fields of archaeology, astronomy, biology, geography and physical chemistry will find this book of great benefit. The theories presented are used today in a wide range of subjects from archaeology through to physics, and will provide fascinating reading to anyone engaged in such research. Visit our web page! http://www.wiley.com/

Theory of Spatial Statistics: A Concise Introduction presents the most important models used in spatial statistics, including random fields and point processes, from a rigorous mathematical point of view and shows how to carry out statistical inference. It contains full proofs, real-life examples and theoretical exercises. Solutions to the latter are available in an appendix. Assuming maturity in probability and statistics, these concise lecture notes are self-contained and cover enough material for a semester course. They may also serve as a reference book for researchers. Features * Presents the mathematical foundations of spatial statistics. * Contains worked examples from mining, disease mapping, forestry, soil and environmental science, and criminology. * Gives pointers to the literature to facilitate further study. * Provides example code in R to encourage the student to experiment. * Offers exercises and their solutions to test and deepen understanding. The book is suitable for postgraduate and advanced undergraduate students in mathematics and statistics.

The most important properties of normal and Student t-distributions are presented. A number of applications of these properties are demonstrated. New related results dealing with the distributions of the sum, product and ratio of the independent normal and Student distributions are presented. The materials will be useful to the advanced undergraduate and graduate students and practitioners in the various fields of science and engineering.

Research in the statistical analysis of extreme values has flourished over the past decade: new probability models, inference and data analysis techniques have been introduced; and new application areas have been explored. Statistics of Extremes comprehensively covers a wide range of models and application areas, including risk and insurance: a major area of interest and relevance to extreme value theory. Case studies are introduced providing a good balance of theory and application of each model discussed, incorporating many illustrated examples and plots of data. The last part of the book covers some interesting advanced topics, including time series, regression, multivariate and Bayesian modelling of extremes, the use of which has huge potential.

This empirical research methods course enables informed implementation of statistical procedures, giving rise to trustworthy evidence.

A Comprehensive Handbook of Statistical Concepts, Techniques and Software Tools.

In this book, we provide an easy introduction to Bayesian inference using MCMC techniques, making most topics intuitively reasonable and deriving to appendixes the more complicated matters. The biologist or the agricultural researcher does not normally have a background in Bayesian statistics, having difficulties in following the technical books introducing Bayesian techniques. The difficulties arise from the way of making inferences, which is completely different in the Bayesian school, and from the difficulties in understanding complicated matters such as the MCMC numerical methods. We compare both schools, classic and Bayesian, underlying the advantages of Bayesian solutions, and proposing inferences based in relevant differences, guaranteed values, probabilities of similitude or the use of ratios. We also give a scope of complex problems that can be solved using Bayesian statistics, and we end the book explaining the difficulties associated to model choice and the use of small samples. The book has a practical orientation and uses simple models to introduce the reader in this increasingly popular school of inference.

The lectures that four authors present in this volume investigate core topics related to the accelerated expansion of the Universe. Accelerated expansion occured in the ?36 very early Universe – an exponential expansion in the in ationary period 10 s after the Big Bang. This well-established theoretical concept had rst been p- posed in 1980 by Alan Guth to account for the homogeneity and isotropy of the observable universe, and simultaneously by Alexei Starobinski, and has since then been developed by many authors in great theoretical detail. An accelerated expansion of the late Universe at redshifts z