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A History Of The Central Limit Theorem
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Book Synopsis A History of the Central Limit Theorem by : Hans Fischer
Download or read book A History of the Central Limit Theorem written by Hans Fischer and published by Springer Science & Business Media. This book was released on 2010-10-08 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: This study discusses the history of the central limit theorem and related probabilistic limit theorems from about 1810 through 1950. In this context the book also describes the historical development of analytical probability theory and its tools, such as characteristic functions or moments. The central limit theorem was originally deduced by Laplace as a statement about approximations for the distributions of sums of independent random variables within the framework of classical probability, which focused upon specific problems and applications. Making this theorem an autonomous mathematical object was very important for the development of modern probability theory.
Book Synopsis A History of the Central Limit Theorem by : Hans Fischer
Download or read book A History of the Central Limit Theorem written by Hans Fischer and published by Springer. This book was released on 2012-12-01 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: This study discusses the history of the central limit theorem and related probabilistic limit theorems from about 1810 through 1950. In this context the book also describes the historical development of analytical probability theory and its tools, such as characteristic functions or moments. The central limit theorem was originally deduced by Laplace as a statement about approximations for the distributions of sums of independent random variables within the framework of classical probability, which focused upon specific problems and applications. Making this theorem an autonomous mathematical object was very important for the development of modern probability theory.
Book Synopsis The Life and Times of the Central Limit Theorem by : William J. Adams
Download or read book The Life and Times of the Central Limit Theorem written by William J. Adams and published by American Mathematical Soc.. This book was released on 2009-11-25 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: About the First Edition: The study of any topic becomes more meaningful if one also studies the historical development that resulted in the final theorem. ... This is an excellent book on mathematics in the making. --Philip Peak, The Mathematics Teacher, May, 1975 I find the book very interesting. It contains valuable information and useful references. It can be recommended not only to historians of science and mathematics but also to students of probability and statistics. --Wei-Ching Chang, Historica Mathematica, August, 1976 In the months since I wrote ... I have read it from cover to cover at least once and perused it here and there a number of times. I still find it a very interesting and worthwhile contribution to the history of probability and statistics. --Churchill Eisenhart, past president of the American Statistical Association, in a letter to the author, February 3, 1975 The name Central Limit Theorem covers a wide variety of results involving the determination of necessary and sufficient conditions under which sums of independent random variables, suitably standardized, have cumulative distribution functions close to the Gaussian distribution. As the name Central Limit Theorem suggests, it is a centerpiece of probability theory which also carries over to statistics. Part One of The Life and Times of the Central Limit Theorem, Second Edition traces its fascinating history from seeds sown by Jacob Bernoulli to use of integrals of $\exp (x^2)$ as an approximation tool, the development of the theory of errors of observation, problems in mathematical astronomy, the emergence of the hypothesis of elementary errors, the fundamental work of Laplace, and the emergence of an abstract Central Limit Theorem through the work of Chebyshev, Markov and Lyapunov. This closes the classical period of the life of the Central Limit Theorem, 1713-1901. The second part of the book includes papers by Feller and Le Cam, as well as comments by Doob, Trotter, and Pollard, describing the modern history of the Central Limit Theorem (1920-1937), in particular through contributions of Lindeberg, Cramer, Levy, and Feller. The Appendix to the book contains four fundamental papers by Lyapunov on the Central Limit Theorem, made available in English for the first time.
Book Synopsis Information Theory and the Central Limit Theorem by : Oliver Johnson
Download or read book Information Theory and the Central Limit Theorem written by Oliver Johnson and published by World Scientific. This book was released on 2004 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: Annotation. - Presents surprising, interesting connections between two apparently separate areas of mathematics- Written by one of the researchers who discovered these connections- Offers a new way of looking at familiar results.
Book Synopsis Who Gave You the Epsilon? by : Marlow Anderson
Download or read book Who Gave You the Epsilon? written by Marlow Anderson and published by MAA. This book was released on 2009-03-31 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book picks up the history of mathematics from where Sherlock Holmes in Babylon left it. The 40 articles of Who Gave You the Epsilon? continue the story of the development of mathematics into the nineteenth and twentieth centuries. The articles have all been published in the Mathematical Association of America journals and are in many cases written by distinguished mathematicians such as G. H. Hardy and B. van der Waerden. The articles are arranged thematically to show the development of analysis, geometry, algebra and number theory through this period of time. Each chapter is preceded by a foreword, giving the historical background and setting and the scene, and is followed by an afterword, reporting on advances in our historical knowledge and understanding since the articles first appeared. This book is ideal for anyone wanting to explore the history of mathematics.
Book Synopsis Martingale Limit Theory and Its Application by : P. Hall
Download or read book Martingale Limit Theory and Its Application written by P. Hall and published by Academic Press. This book was released on 2014-07-10 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: Martingale Limit Theory and Its Application discusses the asymptotic properties of martingales, particularly as regards key prototype of probabilistic behavior that has wide applications. The book explains the thesis that martingale theory is central to probability theory, and also examines the relationships between martingales and processes embeddable in or approximated by Brownian motion. The text reviews the martingale convergence theorem, the classical limit theory and analogs, and the martingale limit theorems viewed as the rate of convergence results in the martingale convergence theorem. The book explains the square function inequalities, weak law of large numbers, as well as the strong law of large numbers. The text discusses the reverse martingales, martingale tail sums, the invariance principles in the central limit theorem, and also the law of the iterated logarithm. The book investigates the limit theory for stationary processes via corresponding results for approximating martingales and the estimation of parameters from stochastic processes. The text can be profitably used as a reference for mathematicians, advanced students, and professors of higher mathematics or statistics.
Book Synopsis A History of Parametric Statistical Inference from Bernoulli to Fisher, 1713-1935 by : Anders Hald
Download or read book A History of Parametric Statistical Inference from Bernoulli to Fisher, 1713-1935 written by Anders Hald and published by Springer Science & Business Media. This book was released on 2008-08-24 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a detailed history of parametric statistical inference. Covering the period between James Bernoulli and R.A. Fisher, it examines: binomial statistical inference; statistical inference by inverse probability; the central limit theorem and linear minimum variance estimation by Laplace and Gauss; error theory, skew distributions, correlation, sampling distributions; and the Fisherian Revolution. Lively biographical sketches of many of the main characters are featured throughout, including Laplace, Gauss, Edgeworth, Fisher, and Karl Pearson. Also examined are the roles played by DeMoivre, James Bernoulli, and Lagrange.
Book Synopsis Limit Theorems of Probability Theory by : Yu.V. Prokhorov
Download or read book Limit Theorems of Probability Theory written by Yu.V. Prokhorov and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: A collection of research level surveys on certain topics in probability theory by a well-known group of researchers. The book will be of interest to graduate students and researchers.
Book Synopsis OpenIntro Statistics by : David Diez
Download or read book OpenIntro Statistics written by David Diez and published by . This book was released on 2015-07-02 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The OpenIntro project was founded in 2009 to improve the quality and availability of education by producing exceptional books and teaching tools that are free to use and easy to modify. We feature real data whenever possible, and files for the entire textbook are freely available at openintro.org. Visit our website, openintro.org. We provide free videos, statistical software labs, lecture slides, course management tools, and many other helpful resources.
Book Synopsis A History of Mathematical Statistics from 1750 to 1930 by : Anders Hald
Download or read book A History of Mathematical Statistics from 1750 to 1930 written by Anders Hald and published by Wiley-Interscience. This book was released on 1998-04-22 with total page 832 pages. Available in PDF, EPUB and Kindle. Book excerpt: The long-awaited second volume of Anders Hald's history of the development of mathematical statistics. Anders Hald's A History of Probability and Statistics and Their Applications before 1750 is already considered a classic by many mathematicians and historians. This new volume picks up where its predecessor left off, describing the contemporaneous development and interaction of four topics: direct probability theory and sampling distributions; inverse probability by Bayes and Laplace; the method of least squares and the central limit theorem; and selected topics in estimation theory after 1830. In this rich and detailed work, Hald carefully traces the history of parametric statistical inference, the development of the corresponding mathematical methods, and some typical applications. Not surprisingly, the ideas, concepts, methods, and results of Laplace, Gauss, and Fisher dominate his account. In particular, Hald analyzes the work and interactions of Laplace and Gauss and describes their contributions to modern theory. Hald also offers a great deal of new material on the history of the period and enhances our understanding of both the controversies and continuities that developed between the different schools. To enable readers to compare the contributions of various historical figures, Professor Hald has rewritten the original papers in a uniform modern terminology and notation, while leaving the ideas unchanged. Statisticians, probabilists, actuaries, mathematicians, historians of science, and advanced students will find absorbing reading in the author's insightful description of important problems and how they gradually moved toward solution.
Book Synopsis Statistics Using Technology, Second Edition by : Kathryn Kozak
Download or read book Statistics Using Technology, Second Edition written by Kathryn Kozak and published by Lulu.com. This book was released on 2015-12-12 with total page 459 pages. Available in PDF, EPUB and Kindle. Book excerpt: Statistics With Technology, Second Edition, is an introductory statistics textbook. It uses the TI-83/84 calculator and R, an open source statistical software, for all calculations. Other technology can also be used besides the TI-83/84 calculator and the software R, but these are the ones that are presented in the text. This book presents probability and statistics from a more conceptual approach, and focuses less on computation. Analysis and interpretation of data is more important than how to compute basic statistical values.
Book Synopsis The Concise Encyclopedia of Statistics by : Yadolah Dodge
Download or read book The Concise Encyclopedia of Statistics written by Yadolah Dodge and published by Springer Science & Business Media. This book was released on 2008-04-15 with total page 612 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Concise Encyclopedia of Statistics presents the essential information about statistical tests, concepts, and analytical methods in language that is accessible to practitioners and students of the vast community using statistics in medicine, engineering, physical science, life science, social science, and business/economics. The reference is alphabetically arranged to provide quick access to the fundamental tools of statistical methodology and biographies of famous statisticians. The more than 500 entries include definitions, history, mathematical details, limitations, examples, references, and further readings. All entries include cross-references as well as the key citations. The back matter includes a timeline of statistical inventions. This reference will be an enduring resource for locating convenient overviews about this essential field of study.
Book Synopsis Introductory Business Statistics (hardcover, Full Color) by : Alexander Holmes
Download or read book Introductory Business Statistics (hardcover, Full Color) written by Alexander Holmes and published by . This book was released on 2023-06-30 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Printed in color. Introductory Business Statistics is designed to meet the scope and sequence requirements of the one-semester statistics course for business, economics, and related majors. Core statistical concepts and skills have been augmented with practical business examples, scenarios, and exercises. The result is a meaningful understanding of the discipline, which will serve students in their business careers and real-world experiences.
Book Synopsis Introduction to Probability by : David F. Anderson
Download or read book Introduction to Probability written by David F. Anderson and published by Cambridge University Press. This book was released on 2017-11-02 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: This classroom-tested textbook is an introduction to probability theory, with the right balance between mathematical precision, probabilistic intuition, and concrete applications. Introduction to Probability covers the material precisely, while avoiding excessive technical details. After introducing the basic vocabulary of randomness, including events, probabilities, and random variables, the text offers the reader a first glimpse of the major theorems of the subject: the law of large numbers and the central limit theorem. The important probability distributions are introduced organically as they arise from applications. The discrete and continuous sides of probability are treated together to emphasize their similarities. Intended for students with a calculus background, the text teaches not only the nuts and bolts of probability theory and how to solve specific problems, but also why the methods of solution work.
Book Synopsis Stochastic Limit Theory by : Arnold I. Davidson
Download or read book Stochastic Limit Theory written by Arnold I. Davidson and published by Oxford University Press. This book was released on 1994 with total page 562 pages. Available in PDF, EPUB and Kindle. Book excerpt: This major new econometrics text surveys recent developments in the rapidly expanding field of asymptotic distribution theory, with a special emphasis on the problems of time dependence and heterogeneity. Designed for econometricians and advanced students with limited mathematical training, the book clearly lays out the necessary math and probability theory and uses numerous examples to make its data useful and comprehensible. It also includes original new material from Davidson's own research on central limit theorems. About the Series Advanced Texts in Econometrics is a distinguished and rapidly expanding series in which leading econometricians assess recent developments in such areas as stochastic probability, panel and time series data analysis, modeling, and cointegration. In both hardback and affordable paperback, each volume explains the nature and applicability of a topic in greater depth than possible in introductory textbooks or single journal articles. Each definitive work is formatted to be as accessible and convenient for those who are not familiar with the detailed primary literature.
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.
Book Synopsis Handbook of the Normal Distribution, Second Edition by : Jagdish K. Patel
Download or read book Handbook of the Normal Distribution, Second Edition written by Jagdish K. Patel and published by CRC Press. This book was released on 1996-01-16 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Traces the historical development of the normal law. Second Edition offers a comprehensive treatment of the bivariate normal distribution--presenting entirely new material on normal integrals, asymptotic normality, the asymptotic properties of order statistics, and point estimation and statistical intervals."
