An Introduction to Probability Theory and Its Applications

Author: William Feller

Publisher: John Wiley & Sons

ISBN: N.A

Category: Mathematics

Page: 528

View: 9952

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The nature of probability theory. The sample space. Elements of combinatorial analysis. Fluctuations in coin tossing and random walks. Combination of events. Conditional probability, stochastic independence. The binomial and the Poisson distributions. The Normal approximation to the binomial distribution. Unlimited sequences of Bernoulli trials. Random variables, expectation. Laws of large numbers. Integral valued variables, generating functions. Compound distributions. Branching processes. Recurrent events. Renewal theory. Random walk and ruin problems. Markov chains. Algebraic treatment of finite Markov chains. The simplest time-dependent stochastic processes. Answer to problems. Index.
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Unit Root Tests in Time Series Volume 1

Key Concepts and Problems

Author: K. Patterson

Publisher: Springer

ISBN: 023029930X

Category: Business & Economics

Page: 641

View: 8829

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Testing for a unit root is now an essential part of time series analysis. This volume provides a critical overview and assessment of tests for a unit root in time series, developing the concepts necessary to understand the key theoretical and practical models in unit root testing.
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Statistical Methods with Applications to Demography and Life Insurance

Author: Estáte V. Khmaladze

Publisher: CRC Press

ISBN: 1466505745

Category: Mathematics

Page: 242

View: 9847

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Suitable for statisticians, mathematicians, actuaries, and students interested in the problems of insurance and analysis of lifetimes, Statistical Methods with Applications to Demography and Life Insurance presents contemporary statistical techniques for analyzing life distributions and life insurance problems. It not only contains traditional material but also incorporates new problems and techniques not discussed in existing actuarial literature. The book mainly focuses on the analysis of an individual life and describes statistical methods based on empirical and related processes. Coverage ranges from analyzing the tails of distributions of lifetimes to modeling population dynamics with migrations. To help readers understand the technical points, the text covers topics such as the Stieltjes, Wiener, and Itô integrals. It also introduces other themes of interest in demography, including mixtures of distributions, analysis of longevity and extreme value theory, and the age structure of a population. In addition, the author discusses net premiums for various insurance policies. Mathematical statements are carefully and clearly formulated and proved while avoiding excessive technicalities as much as possible. The book illustrates how these statements help solve numerous statistical problems. It also includes more than 70 exercises.
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Mathematical Statistics

Basic Ideas and Selected Topics, Volume I, Second Edition

Author: Peter J. Bickel,Kjell A. Doksum

Publisher: CRC Press

ISBN: 1498723810

Category: Business & Economics

Page: 576

View: 3452

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Mathematical Statistics: Basic Ideas and Selected Topics, Volume I, Second Edition presents fundamental, classical statistical concepts at the doctorate level. It covers estimation, prediction, testing, confidence sets, Bayesian analysis, and the general approach of decision theory. This edition gives careful proofs of major results and explains ho
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Lectures in Mathematical Statistics

Parts 1 and 2

Author: I͡U. N. Linʹkov

Publisher: American Mathematical Soc.

ISBN: 9780821889688

Category: Mathematics

Page: 321

View: 5558

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This volume is intended for the advanced study of several topics in mathematical statistics. The first part of the book is devoted to sampling theory (from one-dimensional and multidimensional distributions), asymptotic properties of sampling, parameter estimation, sufficient statistics, and statistical estimates. The second part is devoted to hypothesis testing and includes the discussion of families of statistical hypotheses that can be asymptotically distinguished. In particular,the author describes goodness-of-fit and sequential statistical criteria (Kolmogorov, Pearson, Smirnov, and Wald) and studies their main properties. The book is suitable for graduate students and researchers interested in mathematical statistics. It is useful for independent study or supplementaryreading.
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Probability Theory

Author: Alexandr A. Borovkov

Publisher: Springer Science & Business Media

ISBN: 1447152018

Category: Mathematics

Page: 733

View: 8994

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This self-contained, comprehensive book tackles the principal problems and advanced questions of probability theory and random processes in 22 chapters, presented in a logical order but also suitable for dipping into. They include both classical and more recent results, such as large deviations theory, factorization identities, information theory, stochastic recursive sequences. The book is further distinguished by the inclusion of clear and illustrative proofs of the fundamental results that comprise many methodological improvements aimed at simplifying the arguments and making them more transparent. The importance of the Russian school in the development of probability theory has long been recognized. This book is the translation of the fifth edition of the highly successful Russian textbook. This edition includes a number of new sections, such as a new chapter on large deviation theory for random walks, which are of both theoretical and applied interest. The frequent references to Russian literature throughout this work lend a fresh dimension and make it an invaluable source of reference for Western researchers and advanced students in probability related subjects. Probability Theory will be of interest to both advanced undergraduate and graduate students studying probability theory and its applications. It can serve as a basis for several one-semester courses on probability theory and random processes as well as self-study.
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Monte Carlo Statistical Methods

Author: Christian Robert,George Casella

Publisher: Springer Science & Business Media

ISBN: 1475741456

Category: Mathematics

Page: 649

View: 2824

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We have sold 4300 copies worldwide of the first edition (1999). This new edition contains five completely new chapters covering new developments.
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Modern Mathematics for the Engineer: Second Series

Author: Edwin F. Beckenbach

Publisher: Courier Corporation

ISBN: 0486316122

Category: Technology & Engineering

Page: 480

View: 5839

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The second in this two-volume series also contains original papers commissioned from prominent 20th-century mathematicians. A three-part treatment covers mathematical methods, statistical and scheduling studies, and physical phenomena. 1961 edition.
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