Download or read book Characteristic Functions written by E. Lukacs and published by Oxford University Press. This book was released on 1987-03-01 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume studies characteristic functions--which play an essential role in probability and statistics-- for their intrinsic, mathematical interest.
Download or read book Selected Topics in Characteristic Functions written by Nikolai G. Ushakov and published by VSP. This book was released on 1999 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: The series is devoted to the publication of high-level monographs and surveys which cover the whole spectrum of probability and statistics. The books of the series are addressed to both experts and advanced students.
Download or read book Characteristic Functions and Moment Sequences written by Torben Maack Bisgaard and published by Nova Publishers. This book was released on 2000 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains basic information on characteristic functions and moment sequences that is frequently used in probability theory. Characteristic functions and moment sequences are viewed as special cases of positive definite functions. Positive definite functions occur in diverse parts of mathematics, e.g. in operator theory, moment problems, complex function theory, embedding problems, integral equations, and other areas. However, the area of mathematics in which the largest number of people use positive definite functions (some without knowing it) seems to be that of probability theory.
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.
Download or read book Selected Topics in Characteristic Functions written by Nikolai G. Ushakov and published by Walter de Gruyter. This book was released on 2011-11-02 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: The series is devoted to the publication of high-level monographs and surveys which cover the whole spectrum of probability and statistics. The books of the series are addressed to both experts and advanced students.
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.
Download or read book Tables of Characteristic Functions for Solving Boundary value Problems of the Wave Equation with Application to Supersonic Interference written by Jack Norman Nielsen and published by . This book was released on 1957 with total page 682 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tables are presented containing 69,000 values of a set of characteristic functions which first arose in problems of supersonic wing-body interference. The tables are useful in problems of supersonic flow involving aerodynamic shapes which are wholly or in part quasi-cylinders of nearly circular cross section. A number of uses are described in the aerodynamics of bodies alone, body-body or shock-body interference, wing-body interference, the vortex-panel interference. Three illustrative examples are worked out in detail. First, the pressure field due to fuselage indentation is calculated and presented in a form independent of Mach number. Secondly, the tables are applied to a problem involving a previously unpublished solution to the Navier-Stokes equations; namely, the boundary-layer profiles of a circular cylinder moved impulsively with a constant axial force in a viscous incompressible fluid. In the final example, the wave drag of corrugated circular cylinders is calculated as a function of the number of corrugations and their wave length. Several nonaerodynamic applications are pointed out in the fields of acoustics and heat conduction. Generally speaking, the tables are applicable to boundary-value problems of the second kind involving the wave equation in three dimensions with approximately circular cylindrical boundaries or involving the unsteady heat-conduction equation in two space dimensions with nearly circular boundaries.
Download or read book Probability Essentials written by Jean Jacod and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction can be used, at the beginning graduate level, for a one-semester course on probability theory or for self-direction without benefit of a formal course; the measure theory needed is developed in the text. It will also be useful for students and teachers in related areas such as finance theory, electrical engineering, and operations research. The text covers the essentials in a directed and lean way with 28 short chapters, and assumes only an undergraduate background in mathematics. Readers are taken right up to a knowledge of the basics of Martingale Theory, and the interested student will be ready to continue with the study of more advanced topics, such as Brownian Motion and Ito Calculus, or Statistical Inference.
Download or read book Handbook of Probability written by Ionut Florescu and published by John Wiley & Sons. This book was released on 2013-10-28 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: THE COMPLETE COLLECTION NECESSARY FOR A CONCRETE UNDERSTANDING OF PROBABILITY Written in a clear, accessible, and comprehensive manner, the Handbook of Probability presents the fundamentals of probability with an emphasis on the balance of theory, application, and methodology. Utilizing basic examples throughout, the handbook expertly transitions between concepts and practice to allow readers an inclusive introduction to the field of probability. The book provides a useful format with self-contained chapters, allowing the reader easy and quick reference. Each chapter includes an introduction, historical background, theory and applications, algorithms, and exercises. The Handbook of Probability offers coverage of: Probability Space Probability Measure Random Variables Random Vectors in Rn Characteristic Function Moment Generating Function Gaussian Random Vectors Convergence Types Limit Theorems The Handbook of Probability is an ideal resource for researchers and practitioners in numerous fields, such as mathematics, statistics, operations research, engineering, medicine, and finance, as well as a useful text for graduate students.
Download or read book Probability written by Alan F. Karr and published by . This book was released on 1993-08-01 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Characteristic Functions of Real Resonators written by V. M. Vakhnin and published by . This book was released on 1954 with total page 6 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Fourier Transforms of Distributions and Their Inverses written by Fritz Oberhettinger and published by Academic Press. This book was released on 2014-07-03 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fourier Transforms of Distributions and Their Inverses: A Collection of Tables is a collection of tables on the integrals of Fourier transforms of distributions and their inverses involving the class of functions which are nonnegative and integrable over the interval. The emphasis is on the probability densities, and a number of examples are provided. This book is organized into two parts and begins with an introduction to those properties of characteristic functions which are important in probability theory, followed by a description of the tables and their use. The first three tables contain Fourier transforms of absolutely continuous distribution functions, namely, even functions (including Legendre functions); functions vanishing identically for negative values of the argument (including arbitrary powers); and functions that do not belong to either of the above classes. The transform pairs are numbered consecutively and arranged systematically according to the analytical character of the frequency function. The next two tables give the inverse transforms of the functions listed in the first and third tables, respectively. This monograph will appeal to students and specialists in the fields of probability and mathematical statistics.
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.
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.
Download or read book Advanced R written by Hadley Wickham and published by CRC Press. This book was released on 2015-09-15 with total page 669 pages. Available in PDF, EPUB and Kindle. Book excerpt: An Essential Reference for Intermediate and Advanced R Programmers Advanced R presents useful tools and techniques for attacking many types of R programming problems, helping you avoid mistakes and dead ends. With more than ten years of experience programming in R, the author illustrates the elegance, beauty, and flexibility at the heart of R. The book develops the necessary skills to produce quality code that can be used in a variety of circumstances. You will learn: The fundamentals of R, including standard data types and functions Functional programming as a useful framework for solving wide classes of problems The positives and negatives of metaprogramming How to write fast, memory-efficient code This book not only helps current R users become R programmers but also shows existing programmers what’s special about R. Intermediate R programmers can dive deeper into R and learn new strategies for solving diverse problems while programmers from other languages can learn the details of R and understand why R works the way it does.
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.
Download or read book Multicriteria Decision Making Under Conditions of Uncertainty written by Petr Ekel and published by John Wiley & Sons. This book was released on 2019-11-07 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: A guide to the various models and methods to multicriteria decision-making in conditions of uncertainty presented in a systematic approach Multicriteria Decision-Making under Conditions of Uncertainty presents approaches that help to answer the fundamental questions at the center of all decision-making problems: "What to do?" and "How to do it?" The book explores methods of representing and handling diverse manifestations of the uncertainty factor and a multicriteria nature of problems that can arise in system design, planning, operation, and control. The authors—noted experts on the topic—and their book covers essential questions, including notions and fundamental concepts of fuzzy sets, models and methods of multiobjective as well as multiattribute decision-making, the classical approach to dealing with uncertainty of information and its generalization for analyzing multicriteria problems in condition of uncertainty, and more. This comprehensive book contains information on "harmonious solutions" in multiobjective problem-solving (analyzing “i>X, F> models), construction and analysis of “i>X, R/i” models, results aimed at generating robust solutions in analyzing multicriteria problems under uncertainty, and more. In addition, the book includes illustrative examples of various applications, including real-world case studies related to the authors’ various industrial projects. This important resource: Explains the design and processing aspect of fuzzy sets, including construction of membership functions, fuzzy numbers, fuzzy relations, aggregation operations, and fuzzy sets transformations Describes models of multiobjective decision-making (“i>X. M/i” models), their analysis on the basis of using the Bellman-Zadeh approach to decision-making in a fuzzy environment, and their diverse applications, including multicriteria allocation of resources Investigates models of multiattribute decision-making (“i>X, R/i” models) and their analysis on the basis of the construction and processing of fuzzy preference relations as well as demonstrating their applications to solve diverse classes of multiattribute problems Explores notions of payoff matrices and fuzzy-set-based generalization and modification of the classic approach to decision-making under conditions of uncertainty to generate robust solutions in analyzing multicriteria problems Written for students, researchers and practitioners in disciplines in which decision-making is of paramount relevance, Multicriteria Decision-Making under Conditions of Uncertainty presents a systematic and current approach that encompasses a range of models and methods as well as new applications.
