On The Convolution Of The Negative Binomial Random Variables

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Econometric Analysis of Count Data

Author : Rainer Winkelmann
Publisher : Springer Science & Business Media
ISBN 13 : 3662041499
Total Pages : 291 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Econometric Analysis of Count Data by : Rainer Winkelmann

Download or read book Econometric Analysis of Count Data written by Rainer Winkelmann and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: The primary objective of this book is to provide an introduction to the econometric modeling of count data for graduate students and researchers. It should serve anyone whose interest lies either in developing the field fur ther, or in applying existing methods to empirical questions. Much of the material included in this book is not specific to economics, or to quantita tive social sciences more generally, but rather extends to disciplines such as biometrics and technometrics. Applications are as diverse as the number of congressional budget vetoes, the number of children in a household, and the number of mechanical defects in a production line. The unifying theme is a focus on regression models in which a dependent count variable is modeled as a function of independent variables which mayor may not be counts as well. The modeling of count data has come of age. Inclusion of some of the fundamental models in basic textbooks, and implementation on standard computer software programs bear witness to that. Based on the standard Poisson regression model, numerous extensions and alternatives have been developed to address the common challenges faced in empirical modeling (unobserved heterogeneity, selectivity, endogeneity, measurement error, and dependent observations in the context of panel data or multivariate data, to name but a few) as well as the challenges that are specific to count data (e. g. , over dispersion and underdispersion).

Univariate Discrete Distributions

Author : Norman L. Johnson
Publisher : John Wiley & Sons
ISBN 13 : 0471715808
Total Pages : 676 pages
Book Rating : 4.4/5 (717 download)

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Book Synopsis Univariate Discrete Distributions by : Norman L. Johnson

Download or read book Univariate Discrete Distributions written by Norman L. Johnson and published by John Wiley & Sons. This book was released on 2005-10-03 with total page 676 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Set Contains: Continuous Multivariate Distributions, Volume 1, Models and Applications, 2nd Edition by Samuel Kotz, N. Balakrishnan and Normal L. Johnson Continuous Univariate Distributions, Volume 1, 2nd Edition by Samuel Kotz, N. Balakrishnan and Normal L. Johnson Continuous Univariate Distributions, Volume 2, 2nd Edition by Samuel Kotz, N. Balakrishnan and Normal L. Johnson Discrete Multivariate Distributions by Samuel Kotz, N. Balakrishnan and Normal L. Johnson Univariate Discrete Distributions, 3rd Edition by Samuel Kotz, N. Balakrishnan and Normal L. Johnson Discover the latest advances in discrete distributions theory The Third Edition of the critically acclaimed Univariate Discrete Distributions provides a self-contained, systematic treatment of the theory, derivation, and application of probability distributions for count data. Generalized zeta-function and q-series distributions have been added and are covered in detail. New families of distributions, including Lagrangian-type distributions, are integrated into this thoroughly revised and updated text. Additional applications of univariate discrete distributions are explored to demonstrate the flexibility of this powerful method. A thorough survey of recent statistical literature draws attention to many new distributions and results for the classical distributions. Approximately 450 new references along with several new sections are introduced to reflect the current literature and knowledge of discrete distributions. Beginning with mathematical, probability, and statistical fundamentals, the authors provide clear coverage of the key topics in the field, including: Families of discrete distributions Binomial distribution Poisson distribution Negative binomial distribution Hypergeometric distributions Logarithmic and Lagrangian distributions Mixture distributions Stopped-sum distributions Matching, occupancy, runs, and q-series distributions Parametric regression models and miscellanea Emphasis continues to be placed on the increasing relevance of Bayesian inference to discrete distribution, especially with regard to the binomial and Poisson distributions. New derivations of discrete distributions via stochastic processes and random walks are introduced without unnecessarily complex discussions of stochastic processes. Throughout the Third Edition, extensive information has been added to reflect the new role of computer-based applications. With its thorough coverage and balanced presentation of theory and application, this is an excellent and essential reference for statisticians and mathematicians.

Combinatorial Methods in Discrete Distributions

Author : Charalambos A. Charalambides
Publisher : John Wiley & Sons
ISBN 13 : 0471733172
Total Pages : 440 pages
Book Rating : 4.4/5 (717 download)

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Book Synopsis Combinatorial Methods in Discrete Distributions by : Charalambos A. Charalambides

Download or read book Combinatorial Methods in Discrete Distributions written by Charalambos A. Charalambides and published by John Wiley & Sons. This book was released on 2005-06-24 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: A unique approach illustrating discrete distribution theory through combinatorial methods This book provides a unique approach by presenting combinatorial methods in tandem with discrete distribution theory. This method, particular to discreteness, allows readers to gain a deeper understanding of theory by using applications to solve problems. The author makes extensive use of the reduction approach to conditional distributions of independent random occupancy numbers, and provides excellent studies of occupancy and sequential occupancy distributions, convolutions of truncated discrete distributions, and compound and mixture distributions. Combinatorial Methods in Discrete Distributions begins with a brief presentation of set theory followed by basic counting principles. Fundamental principles of combinatorics, finite differences, and discrete probability are included to give readers the necessary foundation to the topics presented in the text. A thorough examination of the field is provided and features: Stirling numbers and generalized factorial coefficients Occupancy and sequential occupancy distributions n-fold convolutions of truncated distributions Compound and mixture distributions Thoroughly worked examples aid readers in understanding complex theory and discovering how theory can be applied to solve practical problems. An appendix with hints and answers to the exercises helps readers work through the more complex sections. Reference notes are provided at the end of each chapter, and an extensive bibliography offers readers a resource for additional information on specialized topics.

Infinite Divisibility of Probability Distributions on the Real Line

Author : Fred W. Steutel
Publisher : CRC Press
ISBN 13 : 020301412X
Total Pages : 562 pages
Book Rating : 4.2/5 (3 download)

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Book Synopsis Infinite Divisibility of Probability Distributions on the Real Line by : Fred W. Steutel

Download or read book Infinite Divisibility of Probability Distributions on the Real Line written by Fred W. Steutel and published by CRC Press. This book was released on 2003-10-03 with total page 562 pages. Available in PDF, EPUB and Kindle. Book excerpt: Infinite Divisibility of Probability Distributions on the Real Line reassesses classical theory and presents new developments, while focusing on divisibility with respect to convolution or addition of independent random variables. This definitive, example-rich text supplies approximately 100 examples to correspond with all major chapter topics and reviews infinite divisibility in light of the central limit problem. It contrasts infinite divisibility with finite divisibility, discusses the preservation of infinite divisibility under mixing for many classes of distributions, and investigates self-decomposability and stability on the nonnegative reals, nonnegative integers, and the reals.

Recursions for Convolutions and Compound Distributions with Insurance Applications

Author : Bjoern Sundt
Publisher : Springer Science & Business Media
ISBN 13 : 3540929002
Total Pages : 348 pages
Book Rating : 4.5/5 (49 download)

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Book Synopsis Recursions for Convolutions and Compound Distributions with Insurance Applications by : Bjoern Sundt

Download or read book Recursions for Convolutions and Compound Distributions with Insurance Applications written by Bjoern Sundt and published by Springer Science & Business Media. This book was released on 2009-04-21 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since 1980, methods for recursive evaluation of aggregate claims distributions have received extensive attention in the actuarial literature. This book gives a unified survey of the theory and is intended to be self-contained to a large extent. As the methodology is applicable also outside the actuarial field, it is presented in a general setting, but actuarial applications are used for motivation. The book is divided into two parts. Part I is devoted to univariate distributions, whereas in Part II, the methodology is extended to multivariate settings. Primarily intended as a monograph, this book can also be used as text for courses on the graduate level. Suggested outlines for such courses are given. The book is of interest for actuaries and statisticians working within the insurance and finance industry, as well as for people in other fields like operations research and reliability theory.

Engineering Biostatistics

Author : Brani Vidakovic
Publisher : John Wiley & Sons
ISBN 13 : 1119168961
Total Pages : 995 pages
Book Rating : 4.1/5 (191 download)

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Book Synopsis Engineering Biostatistics by : Brani Vidakovic

Download or read book Engineering Biostatistics written by Brani Vidakovic and published by John Wiley & Sons. This book was released on 2017-11-06 with total page 995 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides a one-stop resource for engineers learning biostatistics using MATLAB® and WinBUGS Through its scope and depth of coverage, this book addresses the needs of the vibrant and rapidly growing bio-oriented engineering fields while implementing software packages that are familiar to engineers. The book is heavily oriented to computation and hands-on approaches so readers understand each step of the programming. Another dimension of this book is in parallel coverage of both Bayesian and frequentist approaches to statistical inference. It avoids taking sides on the classical vs. Bayesian paradigms, and many examples in this book are solved using both methods. The results are then compared and commented upon. Readers have the choice of MATLAB® for classical data analysis and WinBUGS/OpenBUGS for Bayesian data analysis. Every chapter starts with a box highlighting what is covered in that chapter and ends with exercises, a list of software scripts, datasets, and references. Engineering Biostatistics: An Introduction using MATLAB® and WinBUGS also includes: parallel coverage of classical and Bayesian approaches, where appropriate substantial coverage of Bayesian approaches to statistical inference material that has been classroom-tested in an introductory statistics course in bioengineering over several years exercises at the end of each chapter and an accompanying website with full solutions and hints to some exercises, as well as additional materials and examples Engineering Biostatistics: An Introduction using MATLAB® and WinBUGS can serve as a textbook for introductory-to-intermediate applied statistics courses, as well as a useful reference for engineers interested in biostatistical approaches.

Generalized Gamma Convolutions and Related Classes of Distributions and Densities

Author : Lennart Bondesson
Publisher : Springer Science & Business Media
ISBN 13 : 1461229480
Total Pages : 184 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Generalized Gamma Convolutions and Related Classes of Distributions and Densities by : Lennart Bondesson

Download or read book Generalized Gamma Convolutions and Related Classes of Distributions and Densities written by Lennart Bondesson and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: Generalized Gamma convolutions were introduced by Olof Thorin in 1977 and were used by him to show that, in particular, the Lognormal distribution is infinitely divisible. After that a large number of papers rapidly appeared with new results in a somewhat random order. Many of the papers appeared in the Scandinavian Actuarial Journal. This work is an attempt to present the main results on this class of probability distributions and related classes in a rather logical order. The goal has been to be on a level that is not too advanced. However, since the field is rather technical, most readers will find difficult passages in the text. Those who do not want to visit a mysterious land situated between the land of probability theory and statistics and the land of classical analysis should not look at this work. When some years ago I submitted a survey to a journal it was suggested by the editor, K. Krickeberg, that it should be expanded to a book. However, at that time I was rather reluctant to do so since there remained so many problems to be solved or to be solved in a smoother way than before. Moreover, there was at that time some lack of probabilistic interpretations and applications. Many of the problems are now solved but still it is felt that more applications than those presented in the work could be found.

Performance Modeling and Analysis of Communication Networks

Author : Phuoc Tran-Gia
Publisher : BoD – Books on Demand
ISBN 13 : 3958261523
Total Pages : 370 pages
Book Rating : 4.9/5 (582 download)

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Book Synopsis Performance Modeling and Analysis of Communication Networks by : Phuoc Tran-Gia

Download or read book Performance Modeling and Analysis of Communication Networks written by Phuoc Tran-Gia and published by BoD – Books on Demand. This book was released on 2021-10-12 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides an introduction to common methods of performance modeling and analysis of communication systems. These methods form the basis of traffic engineering, teletraffic theory, and analytical system dimensioning. The fundamentals of probability theory, stochastic processes, Markov processes, and embedded Markov chains are presented. Basic queueing models are described with applications in communication networks. Advanced methods are presented that have been frequently used in recent practice, especially discrete-time analysis algorithms, or which go beyond classical performance measures such as Quality of Experience or energy efficiency. Recent examples of modern communication networks include Software Defined Networking and the Internet of Things. Throughout the book, illustrative examples are used to provide practical experience in performance modeling and analysis. Target group: The book is aimed at students and scientists in computer science and technical computer science, operations research, electrical engineering and economics.

Dependence Modeling with Copulas

Author : Harry Joe
Publisher : CRC Press
ISBN 13 : 1466583231
Total Pages : 479 pages
Book Rating : 4.4/5 (665 download)

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Book Synopsis Dependence Modeling with Copulas by : Harry Joe

Download or read book Dependence Modeling with Copulas written by Harry Joe and published by CRC Press. This book was released on 2014-06-26 with total page 479 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dependence Modeling with Copulas covers the substantial advances that have taken place in the field during the last 15 years, including vine copula modeling of high-dimensional data. Vine copula models are constructed from a sequence of bivariate copulas. The book develops generalizations of vine copula models, including common and structured facto

Foundations of Quantum Mechanics in the Light of New Technology

Author : Sachio Ishioka
Publisher : World Scientific
ISBN 13 : 9814282138
Total Pages : 376 pages
Book Rating : 4.8/5 (142 download)

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Book Synopsis Foundations of Quantum Mechanics in the Light of New Technology by : Sachio Ishioka

Download or read book Foundations of Quantum Mechanics in the Light of New Technology written by Sachio Ishioka and published by World Scientific. This book was released on 2009 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the proceedings of the 9th International Symposium on Foundations of Quantum Mechanics in the Light of New Technology (ISQMOCoTOKYO''08) which aims to link the recent advances in technology with fundamental problems in quantum mechanics. It also discusses fundamental problems and issues in quantum physics and places a special emphasis on OC Quantum Coherence and DecoherenceOCO. The proceedings included a special lecture by Prof C N Yang, OC Pseudopotential Method in Cold Atom ResearchOCO, and 75 refereed papers covering the wide range of quantum physics: cold atoms and molecules; spin-Hall effect and anomalous Hall effect; magnetic domain wall dynamics and spin-related phenomena; Dirac fermions in condensed matter; quantum dot systems; entanglement and quantum information processing, qubit manipulations; mechanical properties of confined geometry; precise measurements; novel properties of nano-systems; and fundamental problems in quantum physics. The book will not only serve as a good reference for experts on quantum coherence and decoherence, but also as an introduction for newcomers to this field."

Foundations Of Quantum Mechanics In The Light Of New Technology: Isqm-tokyo '08 - Proceedings Of The 9th International Symposium

Author : Sachio Ishioka
Publisher : World Scientific
ISBN 13 : 9814467030
Total Pages : 376 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Foundations Of Quantum Mechanics In The Light Of New Technology: Isqm-tokyo '08 - Proceedings Of The 9th International Symposium by : Sachio Ishioka

Download or read book Foundations Of Quantum Mechanics In The Light Of New Technology: Isqm-tokyo '08 - Proceedings Of The 9th International Symposium written by Sachio Ishioka and published by World Scientific. This book was released on 2009-06-30 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the proceedings of the 9th International Symposium on Foundations of Quantum Mechanics in the Light of New Technology (ISQM—TOKYO'08) which aims to link the recent advances in technology with fundamental problems in quantum mechanics. It also discusses fundamental problems and issues in quantum physics and places a special emphasis on “Quantum Coherence and Decoherence”.The proceedings included a special lecture by Prof C N Yang, “Pseudopotential Method in Cold Atom Research”, and 75 refereed papers covering the wide range of quantum physics: cold atoms and molecules; spin-Hall effect and anomalous Hall effect; magnetic domain wall dynamics and spin-related phenomena; Dirac fermions in condensed matter; quantum dot systems; entanglement and quantum information processing, qubit manipulations; mechanical properties of confined geometry; precise measurements; novel properties of nano-systems; and fundamental problems in quantum physics.The book will not only serve as a good reference for experts on quantum coherence and decoherence, but also as an introduction for newcomers to this field.

Runs and Scans with Applications

Author : Narayanaswamy Balakrishnan
Publisher : John Wiley & Sons
ISBN 13 : 1118150457
Total Pages : 484 pages
Book Rating : 4.1/5 (181 download)

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Book Synopsis Runs and Scans with Applications by : Narayanaswamy Balakrishnan

Download or read book Runs and Scans with Applications written by Narayanaswamy Balakrishnan and published by John Wiley & Sons. This book was released on 2011-09-20 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt: Expert practical and theoretical coverage of runs and scans This volume presents both theoretical and applied aspects of runs and scans, and illustrates their important role in reliability analysis through various applications from science and engineering. Runs and Scans with Applications presents new and exciting content in a systematic and cohesive way in a single comprehensive volume, complete with relevant approximations and explanations of some limit theorems. The authors provide detailed discussions of both classical and current problems, such as: * Sooner and later waiting time * Consecutive systems * Start-up demonstration testing in life-testing experiments * Learning and memory models * "Match" in genetic codes Runs and Scans with Applications offers broad coverage of the subject in the context of reliability and life-testing settings and serves as an authoritative reference for students and professionals alike.

High-pT Physics in the Heavy Ion Era

Author : Jan Rak
Publisher : Cambridge University Press
ISBN 13 : 1107354447
Total Pages : 399 pages
Book Rating : 4.1/5 (73 download)

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Book Synopsis High-pT Physics in the Heavy Ion Era by : Jan Rak

Download or read book High-pT Physics in the Heavy Ion Era written by Jan Rak and published by Cambridge University Press. This book was released on 2013-04-25 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aimed at graduate students and researchers in the field of high-energy nuclear physics, this book provides an overview of the basic concepts of large transverse momentum particle physics, with a focus on pQCD phenomena. It examines high-pT probes of relativistic heavy-ion collisions and will serve as a handbook for those working on RHIC and LHC data analyses. Starting with an introduction and review of the field, the authors look at basic observables and experimental techniques, concentrating on relativistic particle kinematics, before moving onto a discussion about the origins of high-pT physics. The main features of high-pT physics are placed within a historical context and the authors adopt an experimental outlook, highlighting the most important discoveries leading up to the foundation of modern QCD theory. Advanced methods are described in detail, making this book especially useful for newcomers to the field.

Methods in Algorithmic Analysis

Author : Vladimir A. Dobrushkin
Publisher : CRC Press
ISBN 13 : 142006830X
Total Pages : 824 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Methods in Algorithmic Analysis by : Vladimir A. Dobrushkin

Download or read book Methods in Algorithmic Analysis written by Vladimir A. Dobrushkin and published by CRC Press. This book was released on 2016-03-09 with total page 824 pages. Available in PDF, EPUB and Kindle. Book excerpt: Explores the Impact of the Analysis of Algorithms on Many Areas within and beyond Computer Science A flexible, interactive teaching format enhanced by a large selection of examples and exercises Developed from the author’s own graduate-level course, Methods in Algorithmic Analysis presents numerous theories, techniques, and methods used for analyzing algorithms. It exposes students to mathematical techniques and methods that are practical and relevant to theoretical aspects of computer science. After introducing basic mathematical and combinatorial methods, the text focuses on various aspects of probability, including finite sets, random variables, distributions, Bayes’ theorem, and Chebyshev inequality. It explores the role of recurrences in computer science, numerical analysis, engineering, and discrete mathematics applications. The author then describes the powerful tool of generating functions, which is demonstrated in enumeration problems, such as probabilistic algorithms, compositions and partitions of integers, and shuffling. He also discusses the symbolic method, the principle of inclusion and exclusion, and its applications. The book goes on to show how strings can be manipulated and counted, how the finite state machine and Markov chains can help solve probabilistic and combinatorial problems, how to derive asymptotic results, and how convergence and singularities play leading roles in deducing asymptotic information from generating functions. The final chapter presents the definitions and properties of the mathematical infrastructure needed to accommodate generating functions. Accompanied by more than 1,000 examples and exercises, this comprehensive, classroom-tested text develops students’ understanding of the mathematical methodology behind the analysis of algorithms. It emphasizes the important relation between continuous (classical) mathematics and discrete mathematics, which is the basis of computer science.

Stochastics

Author : Hans-Otto Georgii
Publisher : Walter de Gruyter
ISBN 13 : 9783110191455
Total Pages : 384 pages
Book Rating : 4.1/5 (914 download)

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Book Synopsis Stochastics by : Hans-Otto Georgii

Download or read book Stochastics written by Hans-Otto Georgii and published by Walter de Gruyter. This book was released on 2008 with total page 384 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.

Basics of Probability and Stochastic Processes

Author : Esra Bas
Publisher : Springer Nature
ISBN 13 : 3030323234
Total Pages : 303 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Basics of Probability and Stochastic Processes by : Esra Bas

Download or read book Basics of Probability and Stochastic Processes written by Esra Bas and published by Springer Nature. This book was released on 2019-11-05 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook explores probability and stochastic processes at a level that does not require any prior knowledge except basic calculus. It presents the fundamental concepts in a step-by-step manner, and offers remarks and warnings for deeper insights. The chapters include basic examples, which are revisited as the new concepts are introduced. To aid learning, figures and diagrams are used to help readers grasp the concepts, and the solutions to the exercises and problems. Further, a table format is also used where relevant for better comparison of the ideas and formulae. The first part of the book introduces readers to the essentials of probability, including combinatorial analysis, conditional probability, and discrete and continuous random variable. The second part then covers fundamental stochastic processes, including point, counting, renewal and regenerative processes, the Poisson process, Markov chains, queuing models and reliability theory. Primarily intended for undergraduate engineering students, it is also useful for graduate-level students wanting to refresh their knowledge of the basics of probability and stochastic processes.

Statistical Methods for Spatial Data Analysis

Author : Oliver Schabenberger
Publisher : CRC Press
ISBN 13 : 1482258137
Total Pages : 507 pages
Book Rating : 4.4/5 (822 download)

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Book Synopsis Statistical Methods for Spatial Data Analysis by : Oliver Schabenberger

Download or read book Statistical Methods for Spatial Data Analysis written by Oliver Schabenberger and published by CRC Press. This book was released on 2017-01-27 with total page 507 pages. Available in PDF, EPUB and Kindle. Book excerpt: Understanding spatial statistics requires tools from applied and mathematical statistics, linear model theory, regression, time series, and stochastic processes. It also requires a mindset that focuses on the unique characteristics of spatial data and the development of specialized analytical tools designed explicitly for spatial data analysis. Statistical Methods for Spatial Data Analysis answers the demand for a text that incorporates all of these factors by presenting a balanced exposition that explores both the theoretical foundations of the field of spatial statistics as well as practical methods for the analysis of spatial data. This book is a comprehensive and illustrative treatment of basic statistical theory and methods for spatial data analysis, employing a model-based and frequentist approach that emphasizes the spatial domain. It introduces essential tools and approaches including: measures of autocorrelation and their role in data analysis; the background and theoretical framework supporting random fields; the analysis of mapped spatial point patterns; estimation and modeling of the covariance function and semivariogram; a comprehensive treatment of spatial analysis in the spectral domain; and spatial prediction and kriging. The volume also delivers a thorough analysis of spatial regression, providing a detailed development of linear models with uncorrelated errors, linear models with spatially-correlated errors and generalized linear mixed models for spatial data. It succinctly discusses Bayesian hierarchical models and concludes with reviews on simulating random fields, non-stationary covariance, and spatio-temporal processes. Additional material on the CRC Press website supplements the content of this book. The site provides data sets used as examples in the text, software code that can be used to implement many of the principal methods described and illustrated, and updates to the text itself.