Applications Of Characteristic Functions

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Multivariate Characteristic and Correlation Functions

Author : Zoltán Sasvári
Publisher : Walter de Gruyter
ISBN 13 : 3110223996
Total Pages : 376 pages
Book Rating : 4.1/5 (12 download)

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Book Synopsis Multivariate Characteristic and Correlation Functions by : Zoltán Sasvári

Download or read book Multivariate Characteristic and Correlation Functions written by Zoltán Sasvári and published by Walter de Gruyter. This book was released on 2013-03-22 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: In a certain sense characteristic functions and correlation functions are the same, the common underlying concept is positive definiteness. Many results in probability theory, mathematical statistics and stochastic processes can be derived by using these functions. While there are books on characteristic functions of one variable, books devoting some sections to the multivariate case, and books treating the general case of locally compact groups, interestingly there is no book devoted entirely to the multidimensional case which is extremely important for applications. This book is intended to fill this gap at least partially. It makes the basic concepts and results on multivariate characteristic and correlation functions easily accessible to both students and researchers in a comprehensive manner. The first chapter presents basic results and should be read carefully since it is essential for the understanding of the subsequent chapters. The second chapter is devoted to correlation functions, their applications to stationary processes and some connections to harmonic analysis. In Chapter 3 we deal with several special properties, Chapter 4 is devoted to the extension problem while Chapter 5 contains a few applications. A relatively large appendix comprises topics like infinite products, functional equations, special functions or compact operators.

Applications of Characteristic Functions

Author : Eugene Lukacs
Publisher :
ISBN 13 :
Total Pages : 208 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Applications of Characteristic Functions by : Eugene Lukacs

Download or read book Applications of Characteristic Functions written by Eugene Lukacs and published by . This book was released on 1964 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Lectures on Probability Theory and Mathematical Statistics - 3rd Edition

Author : Marco Taboga
Publisher : Createspace Independent Publishing Platform
ISBN 13 : 9781981369195
Total Pages : 670 pages
Book Rating : 4.3/5 (691 download)

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Book Synopsis Lectures on Probability Theory and Mathematical Statistics - 3rd Edition by : Marco Taboga

Download or read book Lectures on Probability Theory and Mathematical Statistics - 3rd Edition written by Marco Taboga and published by Createspace Independent Publishing Platform. This book was released on 2017-12-08 with total page 670 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is a collection of 80 short and self-contained lectures covering most of the topics that are usually taught in intermediate courses in probability theory and mathematical statistics. There are hundreds of examples, solved exercises and detailed derivations of important results. The step-by-step approach makes the book easy to understand and ideal for self-study. One of the main aims of the book is to be a time saver: it contains several results and proofs, especially on probability distributions, that are hard to find in standard references and are scattered here and there in more specialistic books. The topics covered by the book are as follows. PART 1 - MATHEMATICAL TOOLS: set theory, permutations, combinations, partitions, sequences and limits, review of differentiation and integration rules, the Gamma and Beta functions. PART 2 - FUNDAMENTALS OF PROBABILITY: events, probability, independence, conditional probability, Bayes' rule, random variables and random vectors, expected value, variance, covariance, correlation, covariance matrix, conditional distributions and conditional expectation, independent variables, indicator functions. PART 3 - ADDITIONAL TOPICS IN PROBABILITY THEORY: probabilistic inequalities, construction of probability distributions, transformations of probability distributions, moments and cross-moments, moment generating functions, characteristic functions. PART 4 - PROBABILITY DISTRIBUTIONS: Bernoulli, binomial, Poisson, uniform, exponential, normal, Chi-square, Gamma, Student's t, F, multinomial, multivariate normal, multivariate Student's t, Wishart. PART 5 - MORE DETAILS ABOUT THE NORMAL DISTRIBUTION: linear combinations, quadratic forms, partitions. PART 6 - ASYMPTOTIC THEORY: sequences of random vectors and random variables, pointwise convergence, almost sure convergence, convergence in probability, mean-square convergence, convergence in distribution, relations between modes of convergence, Laws of Large Numbers, Central Limit Theorems, Continuous Mapping Theorem, Slutsky's Theorem. PART 7 - FUNDAMENTALS OF STATISTICS: statistical inference, point estimation, set estimation, hypothesis testing, statistical inferences about the mean, statistical inferences about the variance.

The Normal Distribution

Author : Wlodzimierz Bryc
Publisher : Springer Science & Business Media
ISBN 13 : 1461225604
Total Pages : 142 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis The Normal Distribution by : Wlodzimierz Bryc

Download or read book The Normal Distribution written by Wlodzimierz Bryc and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a concise presentation of the normal distribution on the real line and its counterparts on more abstract spaces, which we shall call the Gaussian distributions. The material is selected towards presenting characteristic properties, or characterizations, of the normal distribution. There are many such properties and there are numerous rel evant works in the literature. In this book special attention is given to characterizations generated by the so called Maxwell's Theorem of statistical mechanics, which is stated in the introduction as Theorem 0.0.1. These characterizations are of interest both intrin sically, and as techniques that are worth being aware of. The book may also serve as a good introduction to diverse analytic methods of probability theory. We use characteristic functions, tail estimates, and occasionally dive into complex analysis. In the book we also show how the characteristic properties can be used to prove important results about the Gaussian processes and the abstract Gaussian vectors. For instance, in Section 5.4 we present Fernique's beautiful proofs of the zero-one law and of the integrability of abstract Gaussian vectors. The central limit theorem is obtained via characterizations in Section 7.3.

Applied Data Analytics - Principles and Applications

Author : Johnson I Agbinya
Publisher :
ISBN 13 : 9788770043533
Total Pages : 0 pages
Book Rating : 4.0/5 (435 download)

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Book Synopsis Applied Data Analytics - Principles and Applications by : Johnson I Agbinya

Download or read book Applied Data Analytics - Principles and Applications written by Johnson I Agbinya and published by . This book was released on 2024-10-21 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book contains a mixture of machine learning foundations, deep learning, artificial intelligence, statistics and evolutionary learning mathematics written from the usage point of view with rich explanations on what the concepts mean.

Elements of Probability Theory

Author : L. Z. Rumshiskii
Publisher : Elsevier
ISBN 13 : 1483136000
Total Pages : 173 pages
Book Rating : 4.4/5 (831 download)

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Book Synopsis Elements of Probability Theory by : L. Z. Rumshiskii

Download or read book Elements of Probability Theory written by L. Z. Rumshiskii and published by Elsevier. This book was released on 2016-06-06 with total page 173 pages. Available in PDF, EPUB and Kindle. Book excerpt: Elements of Probability Theory focuses on the basic ideas and methods of the theory of probability. The book first discusses events and probabilities, including the classical meaning of probability, fundamental properties of probabilities, and the primary rule for the multiplication of probabilities. The text also touches on random variables and probability distributions. Topics include discrete and random variables; functions of random variables; and binomial distributions. The selection also discusses the numerical characteristics of probability distributions; limit theorems and estimates of the mean; and the law of large numbers. The text also describes linear correlation, including conditional expectations and their properties, coefficient of correlation, and best linear approximation to the regression function. The book presents tables that show the values of the normal probability integral, Poisson distribution, and values of the normal probability density. The text is a good source of data for readers and students interested in probability theory.

Probability for Statistics and Machine Learning

Author : Anirban DasGupta
Publisher : Springer Science & Business Media
ISBN 13 : 1441996346
Total Pages : 796 pages
Book Rating : 4.4/5 (419 download)

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Book Synopsis Probability for Statistics and Machine Learning by : Anirban DasGupta

Download or read book Probability for Statistics and Machine Learning written by Anirban DasGupta and published by Springer Science & Business Media. This book was released on 2011-05-17 with total page 796 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a versatile and lucid treatment of classic as well as modern probability theory, while integrating them with core topics in statistical theory and also some key tools in machine learning. It is written in an extremely accessible style, with elaborate motivating discussions and numerous worked out examples and exercises. The book has 20 chapters on a wide range of topics, 423 worked out examples, and 808 exercises. It is unique in its unification of probability and statistics, its coverage and its superb exercise sets, detailed bibliography, and in its substantive treatment of many topics of current importance. This book can be used as a text for a year long graduate course in statistics, computer science, or mathematics, for self-study, and as an invaluable research reference on probabiliity and its applications. Particularly worth mentioning are the treatments of distribution theory, asymptotics, simulation and Markov Chain Monte Carlo, Markov chains and martingales, Gaussian processes, VC theory, probability metrics, large deviations, bootstrap, the EM algorithm, confidence intervals, maximum likelihood and Bayes estimates, exponential families, kernels, and Hilbert spaces, and a self contained complete review of univariate probability.

Theory of Random Functions

Author : V. S. Pugachev
Publisher : Elsevier
ISBN 13 : 1483156257
Total Pages : 852 pages
Book Rating : 4.4/5 (831 download)

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Book Synopsis Theory of Random Functions by : V. S. Pugachev

Download or read book Theory of Random Functions written by V. S. Pugachev and published by Elsevier. This book was released on 2013-10-22 with total page 852 pages. Available in PDF, EPUB and Kindle. Book excerpt: Theory of Random Functions and Its Application to Control Problems presents insights into a branch of probability theory, the theory of random functions, which studies and takes into account the effects of random factors on the functioning of control systems. The book does not require a high level of competency in the use of mathematical techniques and explains the basics of probability theory before focusing on the concepts of the theory of random functions. The selection also discusses in great detail the aspects of random functions and provides chapters that cover the determination and solution to problems of optimal systems. The text will be of value to telecommunications engineers, aeronautical engineers, meteorologists, seismologists, and other professionals engaged in applied sciences.

A Modern Approach to Probability Theory

Author : Bert E. Fristedt
Publisher : Springer Science & Business Media
ISBN 13 : 1489928375
Total Pages : 775 pages
Book Rating : 4.4/5 (899 download)

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Book Synopsis A Modern Approach to Probability Theory by : Bert E. Fristedt

Download or read book A Modern Approach to Probability Theory written by Bert E. Fristedt and published by Springer Science & Business Media. This book was released on 2013-11-21 with total page 775 pages. Available in PDF, EPUB and Kindle. Book excerpt: Students and teachers of mathematics and related fields will find this book a comprehensive and modern approach to probability theory, providing the background and techniques to go from the beginning graduate level to the point of specialization in research areas of current interest. The book is designed for a two- or three-semester course, assuming only courses in undergraduate real analysis or rigorous advanced calculus, and some elementary linear algebra. A variety of applications—Bayesian statistics, financial mathematics, information theory, tomography, and signal processing—appear as threads to both enhance the understanding of the relevant mathematics and motivate students whose main interests are outside of pure areas.

Counterexamples in Probability

Author : Jordan M. Stoyanov
Publisher : Courier Corporation
ISBN 13 : 0486499987
Total Pages : 404 pages
Book Rating : 4.4/5 (864 download)

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Book Synopsis Counterexamples in Probability by : Jordan M. Stoyanov

Download or read book Counterexamples in Probability written by Jordan M. Stoyanov and published by Courier Corporation. This book was released on 2014-01-15 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: "While most mathematical examples illustrate the truth of a statement, counterexamples demonstrate a statement's falsity. Enjoyable topics of study, counterexamples are valuable tools for teaching and learning. The definitive book on the subject in regards to probability, this third edition features the author's revisions and corrections plus a substantial new appendix. 2013 edition"--

Probability, Random Variables, and Random Processes

Author : John J. Shynk
Publisher : John Wiley & Sons
ISBN 13 : 1118393953
Total Pages : 850 pages
Book Rating : 4.1/5 (183 download)

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Book Synopsis Probability, Random Variables, and Random Processes by : John J. Shynk

Download or read book Probability, Random Variables, and Random Processes written by John J. Shynk and published by John Wiley & Sons. This book was released on 2012-10-15 with total page 850 pages. Available in PDF, EPUB and Kindle. Book excerpt: Probability, Random Variables, and Random Processes is a comprehensive textbook on probability theory for engineers that provides a more rigorous mathematical framework than is usually encountered in undergraduate courses. It is intended for first-year graduate students who have some familiarity with probability and random variables, though not necessarily of random processes and systems that operate on random signals. It is also appropriate for advanced undergraduate students who have a strong mathematical background. The book has the following features: Several appendices include related material on integration, important inequalities and identities, frequency-domain transforms, and linear algebra. These topics have been included so that the book is relatively self-contained. One appendix contains an extensive summary of 33 random variables and their properties such as moments, characteristic functions, and entropy. Unlike most books on probability, numerous figures have been included to clarify and expand upon important points. Over 600 illustrations and MATLAB plots have been designed to reinforce the material and illustrate the various characterizations and properties of random quantities. Sufficient statistics are covered in detail, as is their connection to parameter estimation techniques. These include classical Bayesian estimation and several optimality criteria: mean-square error, mean-absolute error, maximum likelihood, method of moments, and least squares. The last four chapters provide an introduction to several topics usually studied in subsequent engineering courses: communication systems and information theory; optimal filtering (Wiener and Kalman); adaptive filtering (FIR and IIR); and antenna beamforming, channel equalization, and direction finding. This material is available electronically at the companion website. Probability, Random Variables, and Random Processes is the only textbook on probability for engineers that includes relevant background material, provides extensive summaries of key results, and extends various statistical techniques to a range of applications in signal processing.

A History of the Mathematical Theory of Probability

Author : Isaac Todhunter
Publisher :
ISBN 13 :
Total Pages : 652 pages
Book Rating : 4.B/5 (1 download)

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Book Synopsis A History of the Mathematical Theory of Probability by : Isaac Todhunter

Download or read book A History of the Mathematical Theory of Probability written by Isaac Todhunter and published by . This book was released on 1865 with total page 652 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Probability-Based Structural Fire Load

Author : Leo Razdolsky
Publisher : Cambridge University Press
ISBN 13 : 110703874X
Total Pages : 353 pages
Book Rating : 4.1/5 (7 download)

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Book Synopsis Probability-Based Structural Fire Load by : Leo Razdolsky

Download or read book Probability-Based Structural Fire Load written by Leo Razdolsky and published by Cambridge University Press. This book was released on 2014-08-25 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the subject of probabilistic analysis to engineers and can be used as a reference in applying this technology.

Fourier Analysis in Probability Theory

Author : Tatsuo Kawata
Publisher : Academic Press
ISBN 13 : 148321852X
Total Pages : 681 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Fourier Analysis in Probability Theory by : Tatsuo Kawata

Download or read book Fourier Analysis in Probability Theory written by Tatsuo Kawata and published by Academic Press. This book was released on 2014-06-17 with total page 681 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fourier Analysis in Probability Theory provides useful results from the theories of Fourier series, Fourier transforms, Laplace transforms, and other related studies. This 14-chapter work highlights the clarification of the interactions and analogies among these theories. Chapters 1 to 8 present the elements of classical Fourier analysis, in the context of their applications to probability theory. Chapters 9 to 14 are devoted to basic results from the theory of characteristic functions of probability distributors, the convergence of distribution functions in terms of characteristic functions, and series of independent random variables. This book will be of value to mathematicians, engineers, teachers, and students.

Characteristic Functions, Scattering Functions and Transfer Functions

Author : Daniel Alpay
Publisher : Springer Science & Business Media
ISBN 13 : 3034601832
Total Pages : 393 pages
Book Rating : 4.0/5 (346 download)

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Book Synopsis Characteristic Functions, Scattering Functions and Transfer Functions by : Daniel Alpay

Download or read book Characteristic Functions, Scattering Functions and Transfer Functions written by Daniel Alpay and published by Springer Science & Business Media. This book was released on 2010-01-12 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: Transfer functions and characteristic functions proved to be key in operator theory and system theory. Moshe Livic played a major role in developing these functions, and this book of papers dedicated to his memory covers a wide variety of topics in the field.

Probability Theory

Author : R.G. Laha
Publisher : Courier Dover Publications
ISBN 13 : 0486842304
Total Pages : 576 pages
Book Rating : 4.4/5 (868 download)

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Book Synopsis Probability Theory by : R.G. Laha

Download or read book Probability Theory written by R.G. Laha and published by Courier Dover Publications. This book was released on 2020-05-21 with total page 576 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive presentation of the basic concepts of probability theory examines both classical and modern methods. The treatment emphasizes the relationship between probability theory and mathematical analysis, and it stresses applications to statistics as well as to analysis. Topics include: • The laws of large numbers • Distribution and characteristic functions • The central limit problem • Dependence • Random variables taking values in a normed linear space Each chapter features worked examples in addition to problems, and bibliographical references to supplementary reading material enhance the text. For advanced undergraduates and graduate students in mathematics.

Probability

Author : Rick Durrett
Publisher : Cambridge University Press
ISBN 13 : 113949113X
Total Pages : pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Probability by : Rick Durrett

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.