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 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 Probability written by Rick Durrett and published by Cambridge University Press. This book was released on 2010-08-30 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This classic introduction to probability theory for beginning graduate students covers laws of large numbers, central limit theorems, random walks, martingales, Markov chains, ergodic theorems, and Brownian motion. It is a comprehensive treatment concentrating on the results that are the most useful for applications. Its philosophy is that the best way to learn probability is to see it in action, so there are 200 examples and 450 problems. The fourth edition begins with a short chapter on measure theory to orient readers new to the subject.
Download or read book The Conway Maxwell Poisson Distribution written by Kimberly F. Sellers and published by Cambridge University Press. This book was released on 2023-02-28 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: While the Poisson distribution is a classical statistical model for count data, the distributional model hinges on the constraining property that its mean equal its variance. This text instead introduces the Conway-Maxwell-Poisson distribution and motivates its use in developing flexible statistical methods based on its distributional form. This two-parameter model not only contains the Poisson distribution as a special case but, in its ability to account for data over- or under-dispersion, encompasses both the geometric and Bernoulli distributions. The resulting statistical methods serve in a multitude of ways, from an exploratory data analysis tool, to a flexible modeling impetus for varied statistical methods involving count data. The first comprehensive reference on the subject, this text contains numerous illustrative examples demonstrating R code and output. It is essential reading for academics in statistics and data science, as well as quantitative researchers and data analysts in economics, biostatistics and other applied disciplines.
Download or read book Introducing Statistics written by Graham Upton and published by Oxford University Press. This book was released on 2001-01-18 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introducing Statistics has been revised to meet the requirements of all the new A Level specifications. It covers in one volume all the statistics required by students taking single-subject Advanced Level Mathematics and also provides the basis for a first course in statistics in higher education. This is a highly accessible resource, supported by clear illustrations, nearly 200 worked examples, and packed with examination style questions. Suggestions for practical work and for calculator and computer exercises are included.
Download or read book Poisson Approximation written by A. D. Barbour and published by . This book was released on 2023 with total page 0 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. 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.
Download or read book Probability Approximations via the Poisson Clumping Heuristic written by David Aldous and published by Springer. This book was released on 2010-12-01 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Introductory Business Statistics hardcover Full Color written by Alexander Holmes and published by . This book was released on 2023-06-30 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Printed in color. 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.
Download or read book Scan Statistics written by Joseph Glaz and published by Springer Science & Business Media. This book was released on 2009-12-24 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: Scan statistics is currently one of the most active and important areas of research in applied probability and statistics, having applications to a wide variety of fields: archaeology, astronomy, bioinformatics, biosurveillance, molecular biology, genetics, computer science, electrical engineering, geography, material sciences, physics, reconnaissance, reliability and quality control, telecommunication, and epidemiology. Filling a gap in the literature, this self-contained volume brings together a collection of selected chapters illustrating the depth and diversity of theory, methods and applications in the area of scan statistics.
Download or read book Lectures on the Poisson Process written by Günter Last and published by Cambridge University Press. This book was released on 2017-10-26 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: A modern introduction to the Poisson process, with general point processes and random measures, and applications to stochastic geometry.
Download or read book Asymptotic Theory of Statistics and Probability written by Anirban DasGupta and published by Springer Science & Business Media. This book was released on 2008-03-07 with total page 726 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique book delivers an encyclopedic treatment of classic as well as contemporary large sample theory, dealing with both statistical problems and probabilistic issues and tools. The book is unique in its detailed coverage of fundamental topics. It is written in an extremely lucid style, with an emphasis on the conceptual discussion of the importance of a problem and the impact and relevance of the theorems. There is no other book in large sample theory that matches this book in coverage, exercises and examples, bibliography, and lucid conceptual discussion of issues and theorems.
Download or read book Probability Towards 2000 written by L. Accardi and published by Springer Science & Business Media. This book was released on 1998-03-27 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: Senior probabilists from around the world with widely differing specialities gave their visions of the state of their specialty, why they think it is important, and how they think it will develop in the new millenium. The volume includes papers given at a symposium at Columbia University in 1995, but papers from others not at the meeting were added to broaden the coverage of areas. All papers were refereed.
Download or read book Approximations to the Poisson Binomial and Hypergeometric Distribution Functions written by W. Molenaar and published by . This book was released on 1970 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Fundamentals of Probability A First Course written by Anirban DasGupta and published by Springer Science & Business Media. This book was released on 2010-04-02 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: Probability theory is one branch of mathematics that is simultaneously deep and immediately applicable in diverse areas of human endeavor. It is as fundamental as calculus. Calculus explains the external world, and probability theory helps predict a lot of it. In addition, problems in probability theory have an innate appeal, and the answers are often structured and strikingly beautiful. A solid background in probability theory and probability models will become increasingly more useful in the twenty-?rst century, as dif?cult new problems emerge, that will require more sophisticated models and analysis. Thisisa text onthe fundamentalsof thetheoryofprobabilityat anundergraduate or ?rst-year graduate level for students in science, engineering,and economics. The only mathematical background required is knowledge of univariate and multiva- ate calculus and basic linear algebra. The book covers all of the standard topics in basic probability, such as combinatorial probability, discrete and continuous distributions, moment generating functions, fundamental probability inequalities, the central limit theorem, and joint and conditional distributions of discrete and continuous random variables. But it also has some unique features and a forwa- looking feel.
Download or read book Stochastics written by Hans-Otto Georgii and published by Walter de Gruyter. This book was released on 2008-08-27 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a translation of the third edition of the well accepted German textbook 'Stochastik', which presents the fundamental ideas and results of both probability theory and statistics, and comprises the material of a one-year course. The stochastic concepts, models and methods are motivated by examples and problems and then developed and analysed systematically.
Download or read book Quantitative Techniques for Managerial Decisions written by U. K. Srivastava and published by New Age International. This book was released on 1989 with total page 962 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Book Is Designed To Serve As A Text For Management, Economics, Accountancy (Chartered And Cost Accountancy), And Commerce Students. The Book Covers Concepts, Illustrations And Problems In Statistics And Operations Research. Part I Deals With Statistical Techniques For Decision Making. Part Ii Studies Various Operations Research Techniques For Managerial Decisions.The Book Contains Illustrations And Problems, Drawn Extensively From Various Functional Areas Of Management, Viz., Production, Finance, Marketing And Personnel, Which Are Designed To Understand Real Life Decision Making Situations. In Order To Make The Book Self-Contained, All Relevant Mathematical Concepts And Their Applications Have Been Included. To Enhance The Understanding Of The Subject Matter By The Students Belonging To Different Disciplines, The Approach Adopted In This Book, Both In Statistics And Operations Research, Is Conceptional Rather Than Mathematical. Hence Complicated Mathematical Proofs Have Been Avoided.This Book Would Be An Ideal Reference To Executives, Computer Professionals, Industrial Engineers, Economic Planners And Social Scientists. The Other Books By The Same Authors Are: Operations Research For Management And Business Statistics.
Download or read book Laws of Small Numbers Extremes and Rare Events written by Michael Falk and published by Springer Science & Business Media. This book was released on 2010-10-07 with total page 513 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the publication of the first edition of this seminar book in 1994, the theory and applications of extremes and rare events have enjoyed an enormous and still increasing interest. The intention of the book is to give a mathematically oriented development of the theory of rare events underlying various applications. This characteristic of the book was strengthened in the second edition by incorporating various new results. In this third edition, the dramatic change of focus of extreme value theory has been taken into account: from concentrating on maxima of observations it has shifted to large observations, defined as exceedances over high thresholds. One emphasis of the present third edition lies on multivariate generalized Pareto distributions, their representations, properties such as their peaks-over-threshold stability, simulation, testing and estimation. Reviews of the 2nd edition: "In brief, it is clear that this will surely be a valuable resource for anyone involved in, or seeking to master, the more mathematical features of this field." David Stirzaker, Bulletin of the London Mathematical Society "Laws of Small Numbers can be highly recommended to everyone who is looking for a smooth introduction to Poisson approximations in EVT and other fields of probability theory and statistics. In particular, it offers an interesting view on multivariate EVT and on EVT for non-iid observations, which is not presented in a similar way in any other textbook." Holger Drees, Metrika
