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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 .
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 ...
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 ...
Pierre Rémond de Montmort, in collaboration with Nicolaus Bernoulli, wrote a book on probability Essay d'analyse sur les jeux de hazard which appeared in 1708, which can be seen as an extension of the Part III of Ars Conjectandi which applies combinatorics and probability to analyze games of chance commonly played at that time. [34]
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.
Theorem of de Moivre–Laplace (probability theory) Theorem of the cube (algebraic varieties) Theorem of the gnomon ; Theorem of three moments ; Theorem on friends and strangers (Ramsey theory) Thévenin's theorem (electrical circuits) Thompson transitivity theorem (finite groups) Thompson uniqueness theorem (finite groups)