Elements of Distribution Theory

Author: Thomas A. Severini
Publisher: Cambridge University Press
ISBN: 1139446118
Format: PDF, Mobi
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This detailed introduction to distribution theory uses no measure theory, making it suitable for students in statistics and econometrics as well as for researchers who use statistical methods. Good backgrounds in calculus and linear algebra are important and a course in elementary mathematical analysis is useful, but not required. An appendix gives a detailed summary of the mathematical definitions and results that are used in the book. Topics covered range from the basic distribution and density functions, expectation, conditioning, characteristic functions, cumulants, convergence in distribution and the central limit theorem to more advanced concepts such as exchangeability, models with a group structure, asymptotic approximations to integrals, orthogonal polynomials and saddlepoint approximations. The emphasis is on topics useful in understanding statistical methodology; thus, parametric statistical models and the distribution theory associated with the normal distribution are covered comprehensively.

Distribution Theory and Applications

Author: Abdellah El Kinani
Publisher: World Scientific
ISBN: 9814304921
Format: PDF, ePub
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The general frame for the resolution of PDEs is the theory of kernels ù the first elements of which are sufficient to show the practicality of distribution theory in applications. --

The Theory of Probability and the Elements of Statistics

Author: Boris Vladimirovich Gnedenko
Publisher: American Mathematical Soc.
ISBN: 9780821837467
Format: PDF, ePub
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This classic book is intended to be the first introduction to probability and statistics written with an emphasis on the analytic approach to the problems discussed. Topics include the axiomatic setup of probability theory, polynomial distribution, finite Markov chains, distribution functions and convolution, the laws of large numbers (weak and strong), characteristic functions, the central limit theorem, infinitely divisible distributions, and Markov processes. Written in a clear and concise style, this book by Gnedenko can serve as a textbook for undergraduate and graduate courses in probability.

Sorting

Author: Hosam M. Mahmoud
Publisher: John Wiley & Sons
ISBN: 111803113X
Format: PDF, ePub, Docs
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A cutting-edge look at the emerging distributional theory ofsorting Research on distributions associated with sorting algorithms hasgrown dramatically over the last few decades, spawning many exactand limiting distributions of complexity measures for many sortingalgorithms. Yet much of this information has been scattered indisparate and highly specialized sources throughout the literature.In Sorting: A Distribution Theory, leading authority Hosam Mahmoudcompiles, consolidates, and clarifies the large volume of availableresearch, providing a much-needed, comprehensive treatment of theentire emerging distributional theory of sorting. Mahmoud carefully constructs a logical framework for the analysisof all standard sorting algorithms, focusing on the development ofthe probability distributions associated with the algorithms, aswell as other issues in probability theory such as measures ofconcentration and rates of convergence. With an emphasis onnarrative rather than technical explanations, this exceptionallywell-written book makes new results easily accessible to a broadspectrum of readers, including computer professionals, scientists,mathematicians, and engineers. Sorting: A DistributionTheory: * Contains introductory material on complete and partialsorting * Explains insertion sort, quick sort, and merge sort, among othermethods * Offers verbal descriptions of the mechanics of the algorithms aswell as the necessary code * Illustrates the distribution theory of sorting using a broadarray of both classical and modern techniques * Features a variety of end-of-chapter exercises

Distribution Theory

Author: Petre Teodorescu
Publisher: John Wiley & Sons
ISBN: 3527653635
Format: PDF, Kindle
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In this comprehensive monograph, the authors apply modern mathematical methods to the study of mechanical and physical phenomena or techniques in acoustics, optics, and electrostatics, where classical mathematical tools fail. They present a general method of approaching problems, pointing out different aspects and difficulties that may occur. With respect to the theory of distributions, only the results and the principle theorems are given as well as some mathematical results. The book also systematically deals with a large number of applications to problems of general Newtonian mechanics, as well as to problems pertaining to the mechanics of deformable solids and physics. Special attention is placed upon the introduction of corresponding mathematical models. Addressed to a wide circle of readers who use mathematical methods in their work: applied mathematicians, engineers in various branches, as well as physicists, while also benefiting students in various fields.

Distribution Theory and Transform Analysis

Author: A.H. Zemanian
Publisher: Courier Corporation
ISBN: 0486151948
Format: PDF, ePub, Docs
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Distribution theory, a relatively recent mathematical approach to classical Fourier analysis, not only opened up new areas of research but also helped promote the development of such mathematical disciplines as ordinary and partial differential equations, operational calculus, transformation theory, and functional analysis. This text was one of the first to give a clear explanation of distribution theory; it combines the theory effectively with extensive practical applications to science and engineering problems. Based on a graduate course given at the State University of New York at Stony Brook, this book has two objectives: to provide a comparatively elementary introduction to distribution theory and to describe the generalized Fourier and Laplace transformations and their applications to integrodifferential equations, difference equations, and passive systems. After an introductory chapter defining distributions and the operations that apply to them, Chapter 2 considers the calculus of distributions, especially limits, differentiation, integrations, and the interchange of limiting processes. Some deeper properties of distributions, such as their local character as derivatives of continuous functions, are given in Chapter 3. Chapter 4 introduces the distributions of slow growth, which arise naturally in the generalization of the Fourier transformation. Chapters 5 and 6 cover the convolution process and its use in representing differential and difference equations. The distributional Fourier and Laplace transformations are developed in Chapters 7 and 8, and the latter transformation is applied in Chapter 9 to obtain an operational calculus for the solution of differential and difference equations of the initial-condition type. Some of the previous theory is applied in Chapter 10 to a discussion of the fundamental properties of certain physical systems, while Chapter 11 ends the book with a consideration of periodic distributions. Suitable for a graduate course for engineering and science students or for a senior-level undergraduate course for mathematics majors, this book presumes a knowledge of advanced calculus and the standard theorems on the interchange of limit processes. A broad spectrum of problems has been included to satisfy the diverse needs of various types of students.

Distribution Theory of Algebraic Numbers

Author: Pei-Chu Hu
Publisher: Walter de Gruyter
ISBN: 3110208261
Format: PDF, Mobi
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The book timely surveys new research results and related developments in Diophantine approximation, a division of number theory which deals with the approximation of real numbers by rational numbers. The book is appended with a list of challenging open problems and a comprehensive list of references. From the contents: Field extensions • Algebraic numbers • Algebraic geometry • Height functions • The abc-conjecture • Roth's theorem • Subspace theorems • Vojta's conjectures • L-functions.

Elements of Large Sample Theory

Author: E.L. Lehmann
Publisher: Springer Science & Business Media
ISBN: 0387227296
Format: PDF, Docs
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Written by one of the main figures in twentieth century statistics, this book provides a unified treatment of first-order large-sample theory. It discusses a broad range of applications including introductions to density estimation, the bootstrap, and the asymptotics of survey methodology. The book is written at an elementary level making it accessible to most readers.

Probability

Author: C. R. Heathcote
Publisher: Courier Corporation
ISBN: 0486153401
Format: PDF
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DIVText deals with basic notions of probablity spaces, random variables, distribution and generating functions, joint distributions and the convergence properties of sequences of random variables. Over 250 exercises with solutions. /div