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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 ...
Abraham de Moivre FRS (French pronunciation: [abʁaam də mwavʁ]; 26 May 1667 – 27 November 1754) was a French mathematician known for de Moivre's formula, a formula that links complex numbers and trigonometry, and for his work on the normal distribution and probability theory.
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 ...
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; De Moivre's formula; ... Poisson distribution This page was last edited on 22 July 2024, at 04:04 (UTC). Text ...
De Moivre's most notable achievement in probability was the discovery of the first instance of central limit theorem, by which he was able to approximate the binomial distribution with the normal distribution. [16] To achieve this De Moivre developed an asymptotic sequence for the factorial function —- which we now refer to as Stirling's ...
de Moivre–Laplace theorem that approximates binomial distribution with a normal distribution Evaluation of several common definite integrals ; [ 13 ] General proof of the Lagrange reversion theorem .
Abraham de Moivre originally discovered this type of integral in 1733, while Gauss published the precise integral in 1809, [1] attributing its discovery to Laplace. The integral has a wide range of applications. For example, with a slight change of variables it is used to compute the normalizing constant of the normal distribution.