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According to the de Moivre–Laplace theorem, as n grows large, the shape of the discrete distribution converges to the continuous Gaussian curve of the normal distribution. In probability theory , the de Moivre–Laplace theorem , which is a special case of the central limit theorem , states that the normal distribution may be used as an ...
The Doctrine of Chances was the first textbook on probability theory, written by 18th-century French mathematician Abraham de Moivre and first published in 1718. [1] De Moivre wrote in English because he resided in England at the time, having fled France to escape the persecution of Huguenots .
This approximation, known as de Moivre–Laplace theorem, is a huge time-saver when undertaking calculations by hand (exact calculations with large n are very onerous); historically, it was the first use of the normal distribution, introduced in Abraham de Moivre's book The Doctrine of Chances in 1738.
De Moivre–Laplace theorem; Lyapunov's central limit theorem; Misconceptions about the normal distribution; Martingale central limit theorem; Infinite divisibility (probability) Method of moments (probability theory) Stability (probability) Stein's lemma; Characteristic function (probability theory) Lévy continuity theorem; Darmois ...
In probability theory and statistics, the Laplace distribution is a continuous probability distribution named after Pierre-Simon Laplace.It is also sometimes called the double exponential distribution, because it can be thought of as two exponential distributions (with an additional location parameter) spliced together along the abscissa, although the term is also sometimes used to refer to ...
The refinement of Bernoulli's Golden Theorem, regarding the convergence of theoretical probability and empirical probability, was taken up by many notable latter day mathematicians like De Moivre, Laplace, Poisson, Chebyshev, Markov, Borel, Cantelli, Kolmogorov and Khinchin.
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The title comes from the contemporary use of the phrase "doctrine of chances" to mean the theory of probability, which had been introduced via the title of a book by Abraham de Moivre. Contemporary reprints of the essay carry a more specific and significant title: A Method of Calculating the Exact Probability of All Conclusions Founded on ...