TY - BOOK ID - 14301962 TI - A History of the Central Limit Theorem : From Classical to Modern Probability Theory PY - 2011 SN - 0387878564 9786612973581 1282973584 0387878572 9780387878560 PB - New York, NY : Springer New York : Imprint: Springer, DB - UniCat KW - Central limit theorem -- History. KW - Central limit theorem KW - Mathematics KW - Physical Sciences & Mathematics KW - Mathematical Statistics KW - History KW - Central limit theorem. KW - Free probability theory. KW - Probability theory, Free KW - Mathematics. KW - History. KW - Probabilities. KW - Statistics. KW - History of Mathematical Sciences. KW - Probability Theory and Stochastic Processes. KW - Statistics, general. KW - Asymptotic distribution (Probability theory) KW - Limit theorems (Probability theory) KW - Operator algebras KW - Selfadjoint operators KW - Distribution (Probability theory. KW - Statistical analysis KW - Statistical data KW - Statistical methods KW - Statistical science KW - Econometrics KW - Distribution functions KW - Frequency distribution KW - Characteristic functions KW - Probabilities KW - StatisticsĀ . KW - Probability KW - Statistical inference KW - Combinations KW - Chance KW - Least squares KW - Mathematical statistics KW - Risk KW - Annals KW - Auxiliary sciences of history KW - Math KW - Science KW - Mathematics - History KW - Distribution (Probability theory) KW - Statistics UR - https://www.unicat.be/uniCat?func=search&query=sysid:14301962 AB - This study aims to embed the history of the central limit theorem within the history of the development of probability theory from its classical to its modern shape, and, more generally, within the corresponding development of mathematics. The history of the central limit theorem is not only expressed in light of "technical" achievement, but is also tied to the intellectual scope of its advancement. The history starts with Laplace's 1810 approximation to distributions of linear combinations of large numbers of independent random variables and its modifications by Poisson, Dirichlet, and Cauchy, and it proceeds up to the discussion of limit theorems in metric spaces by Donsker and Mourier around 1950. This self-contained exposition additionally describes the historical development of analytical probability theory and its tools, such as characteristic functions or moments. The importance of historical connections between the history of analysis and the history of probability theory is demonstrated in great detail. With a thorough discussion of mathematical concepts and ideas of proofs, the reader will be able to understand the mathematical details in light of contemporary development. Special terminology and notations of probability and statistics are used in a modest way and explained in historical context. ER -