Download or read book Compound Poisson Approximation written by V. Čekanavičius and published by CRC Press. This book was released on 2024-08-21 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: Compound Poisson approximation appears naturally in situations where one deals with a large number of rare events. It has important applications in insurance, extreme value theory, reliability theory, mathematical biology, and more. Compound Poisson Approximation synthesizes the most important recent research in the field in a single volume. With an extensive list of references, open problems, and exercises, it will become the standard reference book on the topic. Features • Provides a comprehensive overview of this rapidly expanding field • Synthesizes the most important research results of recent years • Presents an array of special topics • Provides the reader with a set of tools needed for research and education The book is of interest to researchers and postgraduate students from probability, statistics, and mathematics.
Download or read book Compound Poisson Approximation written by Vydas Čekanavičius and published by . This book was released on 2024 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Compound Poisson Approximation appears naturally in situations where one deals with a large number of rare events. It has important applications in insurance, extreme value theory, reliability theory, mathematical biology, etc. This book synthesizes the most important recent research in the field in a single volume. With an extensive list of references, open problems and exercises, it will become the standard reference book on the topic. Features: Provides a comprehensive overview of this rapidly expanding field Synthesizes the most important research results of recent years Presents an array of special topics Provides the reader with a set of tools needed for research and education The book is of interest to researchers and postgraduate students from probability, statistics, and mathematics"--
Download or read book Compound Poisson Approximation for the Distribution of Extremes written by A. D. Barbour and published by . This book was released on 1999 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Compound Poisson Approximation and the Clustering of Random Points written by A. D. Barbour and published by . This book was released on 1998 with total page 21 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Poisson Approximation written by A. D. Barbour and published by . This book was released on 1992 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Poisson "law of small numbers" is a central principle in modern theories of reliability, insurance, and the statistics of extremes. It also has ramifications in apparently unrelated areas, such as the description of algebraic and combinatorial structures, and the distribution of prime numbers. Yet despite its importance, the law of small numbers is only an approximation. In 1975, however, a new technique was introduced, the Stein-Chen method, which makes it possible to estimate the accuracy of the approximation in a wide range of situations. This book provides an introduction to the method, and a varied selection of examples of its application, emphasizing the flexibility of the technique when combined with a judicious choice of coupling. It also contains more advanced material, in particular on compound Poisson and Poisson process approximation, where the reader is brought to the boundaries of current knowledge. The study will be of special interest to postgraduate students and researchers in applied probability as well as computer scientists.
Download or read book Compound Poisson Approximation written by Andrew D. Barbour and published by . This book was released on 2001 with total page 43 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Compound Poisson Approximation for Dissociated Random Variables Via Stein smethod written by Peter Eichelsbacher and published by . This book was released on 1998 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book An Introduction to Stein s Method written by A. D. Barbour and published by World Scientific. This book was released on 2005 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: A common theme in probability theory is the approximation of complicated probability distributions by simpler ones, the central limit theorem being a classical example. Stein's method is a tool which makes this possible in a wide variety of situations. Traditional approaches, for example using Fourier analysis, become awkward to carry through in situations in which dependence plays an important part, whereas Stein's method can often still be applied to great effect. In addition, the method delivers estimates for the error in the approximation, and not just a proof of convergence. Nor is there in principle any restriction on the distribution to be approximated; it can equally well be normal, or Poisson, or that of the whole path of a random process, though the techniques have so far been worked out in much more detail for the classical approximation theorems.This volume of lecture notes provides a detailed introduction to the theory and application of Stein's method, in a form suitable for graduate students who want to acquaint themselves with the method. It includes chapters treating normal, Poisson and compound Poisson approximation, approximation by Poisson processes, and approximation by an arbitrary distribution, written by experts in the different fields. The lectures take the reader from the very basics of Stein's method to the limits of current knowledge.
Download or read book Compound Poisson Approximation for Nonnegative Random Variables Via Stein s Method written by A. D. Barbour and published by . This book was released on 1990 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Compound Poisson Approximation for Markov Chains written by Torkel Erhardsson and published by . This book was released on 1997 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On Accuracy of Multivariate Compound Poisson Approximation written by S. Y. Novak and published by . This book was released on 2000 with total page 9 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Compound Poisson approximation in total variation written by A.D. Barbour and published by . This book was released on 1997 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Stein Chen Method for Compound Poisson Approximation written by Malgorzata Roos and published by . This book was released on 1993 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Stein Chen Method for Compound Poisson Approximation written by Małgorzata S. Roos-Stańko and published by . This book was released on 1993 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Compound Poisson Process Approximation written by Andrew D. Barbour and published by . This book was released on 2001 with total page 41 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Stein s Method and Applications written by A. D. Barbour and published by World Scientific. This book was released on 2005 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stein's startling technique for deriving probability approximations first appeared about 30 years ago. Since then, much has been done to refine and develop the method, but it is still a highly active field of research, with many outstanding problems, both theoretical and in applications. This volume, the proceedings of a workshop held in honour of Charles Stein in Singapore, August 1983, contains contributions from many of the mathematicians at the forefront of this effort. It provides a cross-section of the work currently being undertaken, with many pointers to future directions. The papers in the collection include applications to the study of random binary search trees, Brownian motion on manifolds, Monte-Carlo integration, Edgeworth expansions, regenerative phenomena, the geometry of random point sets, and random matrices.
Download or read book Compound Poisson Approximation for Unbounded Functions on a Group with Application to Large Deviations written by L. H. Y. Chen and published by . This book was released on 1994 with total page 21 pages. Available in PDF, EPUB and Kindle. Book excerpt:
