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Author : A. D. Barbour
Publisher :
ISBN 13 :
Total Pages : 18 pages
Book Rating : 4.:/5 (677 download)
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:
Author : V. Čekanavičius
Publisher : CRC Press
ISBN 13 : 1040037275
Total Pages : 320 pages
Book Rating : 4.0/5 (4 download)
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.
Author : Michael Falk
Publisher : Birkhauser
ISBN 13 :
Total Pages : 298 pages
Book Rating : 4.:/5 (321 download)
Download or read book Laws of Small Numbers written by Michael Falk and published by Birkhauser. This book was released on 1994 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Vydas Čekanavičius
Publisher :
ISBN 13 : 9781032763521
Total Pages : 0 pages
Book Rating : 4.7/5 (635 download)
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"--
Author : A. D. Barbour
Publisher : World Scientific
ISBN 13 : 981256280X
Total Pages : 240 pages
Book Rating : 4.8/5 (125 download)
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.
Author : Serguei Y. Novak
Publisher : CRC Press
ISBN 13 : 1439835748
Total Pages : 402 pages
Book Rating : 4.4/5 (398 download)
Download or read book Extreme Value Methods with Applications to Finance written by Serguei Y. Novak and published by CRC Press. This book was released on 2011-12-20 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Extreme value theory (EVT) deals with extreme (rare) events, which are sometimes reported as outliers. Certain textbooks encourage readers to remove outliers—in other words, to correct reality if it does not fit the model. Recognizing that any model is only an approximation of reality, statisticians are eager to extract information about unknown distribution making as few assumptions as possible. Extreme Value Methods with Applications to Finance concentrates on modern topics in EVT, such as processes of exceedances, compound Poisson approximation, Poisson cluster approximation, and nonparametric estimation methods. These topics have not been fully focused on in other books on extremes. In addition, the book covers: Extremes in samples of random size Methods of estimating extreme quantiles and tail probabilities Self-normalized sums of random variables Measures of market risk Along with examples from finance and insurance to illustrate the methods, Extreme Value Methods with Applications to Finance includes over 200 exercises, making it useful as a reference book, self-study tool, or comprehensive course text. A systematic background to a rapidly growing branch of modern Probability and Statistics: extreme value theory for stationary sequences of random variables.
Author : Peter Eichelsbacher
Publisher :
ISBN 13 :
Total Pages : 16 pages
Book Rating : 4.:/5 (897 download)
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:
Author : R. F. Serfozo
Publisher :
ISBN 13 :
Total Pages : 17 pages
Book Rating : 4.:/5 (227 download)
Download or read book Compound Poisson Approximations for Sums of Random Variables written by R. F. Serfozo and published by . This book was released on 1985 with total page 17 pages. Available in PDF, EPUB and Kindle. Book excerpt: This document shows that a sum of dependent random variables is approximately compound Poisson when the variables are rarely nonzero and, given they are nonzero, their conditional distributions are nearly identical. It give several upper bounds on the total-variation distance between the distribution of such a sum and a compund Poisson distribution. Included is an example for Markovian occurrences of a rare event. The bounds are consistent with those that are known for Poisson approximations for sums of uniformly small random variables. (Author).
Author : A. D. Barbour
Publisher :
ISBN 13 :
Total Pages : 298 pages
Book Rating : 4.3/5 (91 download)
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.
Author : A. D. Barbour
Publisher :
ISBN 13 :
Total Pages : 28 pages
Book Rating : 4.:/5 (897 download)
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:
Author : S. T. Rachev
Publisher :
ISBN 13 :
Total Pages : 29 pages
Book Rating : 4.:/5 (897 download)
Download or read book Approximation of Sums by Compound Poisson Distributions with Respect to Stop-loss Distances written by S. T. Rachev and published by . This book was released on 1990 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : P. van Goethem
Publisher :
ISBN 13 :
Total Pages : 28 pages
Book Rating : 4.:/5 (247 download)
Download or read book Approximation Formulae for Compound Poisson Processes in Case of Claim Distributions Having Infinite Variance Or Infinite Mean written by P. van Goethem and published by . This book was released on 1977 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : P. Van Goethem
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (5 download)
Download or read book Approximation Formulae for Compound Poisson Processes in Case of Claim Distributions Having Infinite Variance Or Infinite Mean written by P. Van Goethem and published by . This book was released on 1979 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Louis Hsiao Yun Chen
Publisher :
ISBN 13 :
Total Pages : 256 pages
Book Rating : 4.F/5 ( download)
Download or read book Poisson Approximation for Sums of Dependent Bernoulli Random Variables written by Louis Hsiao Yun Chen and published by . This book was released on 1971 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Andrew D. Barbour
Publisher :
ISBN 13 :
Total Pages : 43 pages
Book Rating : 4.:/5 (729 download)
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:
Author : P. Van Goethem
Publisher :
ISBN 13 :
Total Pages : 14 pages
Book Rating : 4.:/5 (5 download)
Download or read book Approximation Formulae for Compound Poisson Processes for Some Kind of Claim Distributions Having a Prescribed Asymptotic Behavior written by P. Van Goethem and published by . This book was released on 1977 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : A.D. Barbour
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (955 download)
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:
