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Real Analysis And Probability

Author: Robert B. Ash
Publisher: Academic Press
ISBN: 1483191427
Size: 47.48 MB
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Real Analysis and Probability provides the background in real analysis needed for the study of probability. Topics covered range from measure and integration theory to functional analysis and basic concepts of probability. The interplay between measure theory and topology is also discussed, along with conditional probability and expectation, the central limit theorem, and strong laws of large numbers with respect to martingale theory. Comprised of eight chapters, this volume begins with an overview of the basic concepts of the theory of measure and integration, followed by a presentation of various applications of the basic integration theory. The reader is then introduced to functional analysis, with emphasis on structures that can be defined on vector spaces. Subsequent chapters focus on the connection between measure theory and topology; basic concepts of probability; and conditional probability and expectation. Strong laws of large numbers are also examined, first from the classical viewpoint, and then via martingale theory. The final chapter is devoted to the one-dimensional central limit problem, paying particular attention to the fundamental role of Prokhorov's weak compactness theorem. This book is intended primarily for students taking a graduate course in probability.

Examples And Problems In Mathematical Statistics

Author: Shelemyahu Zacks
Publisher: John Wiley & Sons
ISBN: 1118605837
Size: 69.96 MB
Format: PDF, Kindle
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Provides the necessary skills to solve problems in mathematical statistics through theory, concrete examples, and exercises With a clear and detailed approach to the fundamentals of statistical theory, Examples and Problems in Mathematical Statistics uniquely bridges the gap between theory andapplication and presents numerous problem-solving examples that illustrate the relatednotations and proven results. Written by an established authority in probability and mathematical statistics, each chapter begins with a theoretical presentation to introduce both the topic and the important results in an effort to aid in overall comprehension. Examples are then provided, followed by problems, and finally, solutions to some of the earlier problems. In addition, Examples and Problems in Mathematical Statistics features: Over 160 practical and interesting real-world examples from a variety of fields including engineering, mathematics, and statistics to help readers become proficient in theoretical problem solving More than 430 unique exercises with select solutions Key statistical inference topics, such as probability theory, statistical distributions, sufficient statistics, information in samples, testing statistical hypotheses, statistical estimation, confidence and tolerance intervals, large sample theory, and Bayesian analysis Recommended for graduate-level courses in probability and statistical inference, Examples and Problems in Mathematical Statistics is also an ideal reference for applied statisticians and researchers.

Counterexamples In Probability And Statistics

Author: Joseph P. Romano
Publisher: CRC Press
ISBN: 9780412989018
Size: 19.21 MB
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This volume contains six early mathematical works, four papers on fiducial inference, five on transformations, and twenty-seven on a miscellany of topics in mathematical statistics. Several previously unpublished works are included.

Mathematical Statistics And Data Analysis

Author: John A. Rice
Publisher: Cengage Learning
ISBN: 0534399428
Size: 62.91 MB
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This is the first text in a generation to re-examine the purpose of the mathematical statistics course. The book's approach interweaves traditional topics with data analysis and reflects the use of the computer with close ties to the practice of statistics. The author stresses analysis of data, examines real problems with real data, and motivates the theory. The book's descriptive statistics, graphical displays, and realistic applications stand in strong contrast to traditional texts that are set in abstract settings. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.

Modeling And Analysis Of Compositional Data

Author: Vera Pawlowsky-Glahn
Publisher: John Wiley & Sons
ISBN: 111900313X
Size: 27.87 MB
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Modeling and Analysis of Compositional Data presents a practical and comprehensive introduction to the analysis of compositional data along with numerous examples to illustrate both theory and application of each method. Based upon short courses delivered by the authors, it provides a complete and current compendium of fundamental to advanced methodologies along with exercises at the end of each chapter to improve understanding, as well as data and a solutions manual which is available on an accompanying website. Complementing Pawlowsky-Glahn’s earlier collective text that provides an overview of the state-of-the-art in this field, Modeling and Analysis of Compositional Data fills a gap in the literature for a much-needed manual for teaching, self learning or consulting.

Mathematical Statistics With Applications In R

Author: Kandethody M. Ramachandran
Publisher: Elsevier
ISBN: 012417132X
Size: 68.69 MB
Format: PDF, Docs
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Mathematical Statistics with Applications in R, Second Edition, offers a modern calculus-based theoretical introduction to mathematical statistics and applications. The book covers many modern statistical computational and simulation concepts that are not covered in other texts, such as the Jackknife, bootstrap methods, the EM algorithms, and Markov chain Monte Carlo (MCMC) methods such as the Metropolis algorithm, Metropolis-Hastings algorithm and the Gibbs sampler. By combining the discussion on the theory of statistics with a wealth of real-world applications, the book helps students to approach statistical problem solving in a logical manner. This book provides a step-by-step procedure to solve real problems, making the topic more accessible. It includes goodness of fit methods to identify the probability distribution that characterizes the probabilistic behavior or a given set of data. Exercises as well as practical, real-world chapter projects are included, and each chapter has an optional section on using Minitab, SPSS and SAS commands. The text also boasts a wide array of coverage of ANOVA, nonparametric, MCMC, Bayesian and empirical methods; solutions to selected problems; data sets; and an image bank for students. Advanced undergraduate and graduate students taking a one or two semester mathematical statistics course will find this book extremely useful in their studies. Step-by-step procedure to solve real problems, making the topic more accessible Exercises blend theory and modern applications Practical, real-world chapter projects Provides an optional section in each chapter on using Minitab, SPSS and SAS commands Wide array of coverage of ANOVA, Nonparametric, MCMC, Bayesian and empirical methods

Theoretical Probability For Applications

Author: Sidney C. Port
Publisher: Wiley-Interscience
ISBN: 9780471632160
Size: 72.86 MB
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Offering comprehensive coverage of modern probability theory (exclusive of continuous time stochastic processes), this unique book functions as both an introduction for graduate statisticians, mathematicians, engineers, and economists and an encyclopedic reference of the subject for professionals in these fields. It assumes only a knowledge of calculus as well as basic real analysis and linear algebra. Throughout Theoretical Probability for Applications the focus is on the practical uses of this increasingly important tool. It develops topics of discrete time probability theory for use in a multitude of applications, including stochastic processes, theoretical statistics, and other disciplines that require a sound foundation in modern probability theory. Principles of measure theory related to the study of probability theory are developed as they are required throughout the book. The book examines most of the basic probability models that involve only a finite or countably infinite number of random variables. Topics in the "Discrete Models" section include Bernoulli trials, random walks, matching, sums of indicators, multinomial trials. Poisson approximations and processes, sampling. Markov chains, and discrete renewal theory. Nondiscrete models discussed include univariate, Beta, sampling, and Dirichlet distributions as well as order statistics. A separate chapter covers aspects of the multivariate normal model. Every treatment is carried out for both random vectors and random variables. Consequently, the book contains complete proofs of the vector case which often differ in detail from those of the scalar case. Complete with end-of-chapter exercises that provide both a drill of thematerial presented and an expansion of that same material, explanations of notations used, and a detailed bibliography. Theoretical Probability for Applications is a practical, easy-to-use reference which accommodates the diverse needs of statisticians, mathematicians, economists, engineers, instructors, and students alike.