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Author: A. D. Barbour
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 298
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Book Description
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:
Category : Mathematics
Languages : en
Pages : 298
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Book Description
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: V. Čekanavičius
Publisher: CRC Press
ISBN: 1040037275
Category : Mathematics
Languages : en
Pages : 320
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Book Description
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: David Aldous
Publisher: Springer
ISBN: 9781441930880
Category : Mathematics
Languages : en
Pages : 0
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Book Description
If you place a large number of points randomly in the unit square, what is the distribution of the radius of the largest circle containing no points? Of the smallest circle containing 4 points? Why do Brownian sample paths have local maxima but not points of increase, and how nearly do they have points of increase? Given two long strings of letters drawn i. i. d. from a finite alphabet, how long is the longest consecutive (resp. non-consecutive) substring appearing in both strings? If an imaginary particle performs a simple random walk on the vertices of a high-dimensional cube, how long does it take to visit every vertex? If a particle moves under the influence of a potential field and random perturbations of velocity, how long does it take to escape from a deep potential well? If cars on a freeway move with constant speed (random from car to car), what is the longest stretch of empty road you will see during a long journey? If you take a large i. i. d. sample from a 2-dimensional rotationally-invariant distribution, what is the maximum over all half-spaces of the deviation between the empirical and true distributions? These questions cover a wide cross-section of theoretical and applied probability. The common theme is that they all deal with maxima or min ima, in some sense.
Author: Alexander Holmes
Publisher:
ISBN: 9781998109487
Category :
Languages : en
Pages : 0
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Book Description
Printed in b&w. Introductory Business Statistics is designed to meet the scope and sequence requirements of the one-semester statistics course for business, economics, and related majors. Core statistical concepts and skills have been augmented with practical business examples, scenarios, and exercises. The result is a meaningful understanding of the discipline, which will serve students in their business careers and real-world experiences.
Author: Kimberly F. Sellers
Publisher: Cambridge University Press
ISBN: 1108481108
Category : Mathematics
Languages : en
Pages : 355
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Book Description
This is the first comprehensive introduction to the Conway-Maxwell-Poisson distribution and its contributions in statistical theory and computing in R, including its uses in count data modelling. An essential reference for academics in statistics and data science, as well as quantitative researchers and data analysts in applied disciplines.
Author: A. D. Barbour
Publisher:
ISBN: 9781383023657
Category : Approximation theory
Languages : en
Pages : 0
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Book Description
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. 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.
Author: Openstax
Publisher:
ISBN: 9788565775120
Category : Mathematics
Languages : en
Pages : 914
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Book Description
Introductory Statistics follows scope and sequence requirements of a one-semester introduction to statistics course and is geared toward students majoring in fields other than math or engineering. The text assumes some knowledge of intermediate algebra and focuses on statistics application over theory. Introductory Statistics includes innovative practical applications that make the text relevant and accessible, as well as collaborative exercises, technology integration problems, and statistics labs. Senior Contributing Authors Barbara Illowsky, De Anza College Susan Dean, De Anza College Contributing Authors Daniel Birmajer, Nazareth College Bryan Blount, Kentucky Wesleyan College Sheri Boyd, Rollins College Matthew Einsohn, Prescott College James Helmreich, Marist College Lynette Kenyon, Collin County Community College Sheldon Lee, Viterbo University Jeff Taub, Maine Maritime Academy
Author: A. D. Barbour
Publisher: World Scientific
ISBN: 981256280X
Category : Mathematics
Languages : en
Pages : 240
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Book Description
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: Günter Last
Publisher: Cambridge University Press
ISBN: 1107088011
Category : Mathematics
Languages : en
Pages : 315
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Book Description
A modern introduction to the Poisson process, with general point processes and random measures, and applications to stochastic geometry.
Author: National Academies of Sciences Engineering and Medicine
Publisher:
ISBN: 9780309671576
Category :
Languages : en
Pages :
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Book Description
Marine recreational fishing is a popular activity enjoyed by more than 9 million Americans annually and is a driver of the American ocean-or blue-economy. To ensure that fish populations are not overexploited, the NOAA Fisheries' Marine Recreational Information Program (MRIP) monitors recreational catch through a variety of in-person, telephone, mail-in, and other surveys. NOAA Fisheries' management of recreational catch also must take into account annual catch limits (ACLs) established to prevent overfishing for all managed species in federal waters. While MRIP has worked to improve recreational catch surveys over the past decade, the surveys were never designed to meet the demands of in-season management of ACLs. In some cases, estimates of harvest have triggered accountability measures such as early season closures and reductions in future recreational ACLs, which have been a source of contention with the recreational fishing community. This report presents approaches for optimizing MRIP data and complementary data for in-season management and considers alternatives for managing recreational fisheries with ACLs to better serve both social and economic management objectives.
