The central limit theorem is a fundamental theorem of statistics. In its simplest form, it prescribes that the sum of a sufficiently large number of independent identically distributed random variables approximately follows a normal distribution.
HISTORY
The central limit theorem was first established within the framework of binomial distribution by Moivre, Abraham de (1733). Laplace, Pierre Simon de (1810) formulated the proof of the theorem.
Poisson, Siméon Denis (1824) also worked on this theorem, and Chebyshev, Pafnutii Lvovich (1890–1891) gave a rigorous demonstration of it in the middle of the nineteenth century.
At the beginning of the twentieth century, the Russian mathematician Liapounov, Aleksandr Mikhailovich (1901) created the generally recognized form of the central limit theorem by introducing its characteristic functions. Markov, Andrei Andreevich (1908) also worked on it and was the first to generalize the theorem to the case of independent variables.
According to Le...
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REFERENCE
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Le Cam, L.: The Central Limit Theorem around 1935. Stat. Sci. 1, 78–96 (1986)
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Moivre, A. de: Approximatio ad summam terminorum binomii (a + b)n, in seriem expansi. Supplementum II to Miscellanae Analytica, pp.,1–7 (1733). Photographically reprinted in a rare pamphlet on Moivre and some of his discoveries. Published by Archibald, R.C. Isis 8, 671–683 (1926)
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Tchebychev, P.L. (1890–1891). Sur deux théorèmes relatifs aux probabilités. Acta Math. 14, 305–315
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(2008). Central Limit Theorem. In: The Concise Encyclopedia of Statistics. Springer, New York, NY. https://doi.org/10.1007/978-0-387-32833-1_50
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