Multivariate Probability
Jordan Stoyanov · Journal of the Royal Statistical Society Series A (Statistics in Society) · 2005
The author is known to readers by his previous book ( McColl, 1995), which, as this reviewer is aware, is successfully used at several British universities. Whereas McColl (1995) is devoted to one-dimensional random variables and their distributions, the present book deals with random vectors and hence with multivariate probability distributions. Measure theoretical machinery is deliberately avoided to make the book accessible to a broad readership. In brief, the author's goal is well achieved. The material has been carefully chosen and incorporated into chapters and sections. At the end of the book there is Appendix A (‘Random digits’), Appendix B (‘Normal distribution’), a list of references and an index. Each section contains propositions, examples and exercises. The propositions are given with complete proofs (with a few exceptions, when appropriate references are provided). The examples are fully explained in a way that allows the reader not only to understand the meaning of any of the properties discussed but also to illustrate these properties for specific discrete and/or (absolutely) continuous distributions. It is quite convincing, as the author has done, to start with two-dimensional or three-dimensional distributions, to analyse their basic properties in detail and then to move to distributions of higher dimension. Aspects of simulation are also discussed. Hints or solutions for selected exercises are given at the end of the book.