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Normal Distribution, Univariate

Brief Historical Background

The normal distribution is used extensively in probability theory, statistics, and the natural and social sciences. It is also called the Gaussian distribution because Carl Friedrich Gauss (1809) used it to analyze astronomical data. The normal distribution was (a) first introduced by Abraham de Moivre (1733), as an approximation to a binomial distribution (b) used by Laplace (1774), as an approximation to hypergeometric distribution to analyze errors of experiments and (c) employed, in the past, by Legendre, Peirce, Galton, Lexis, Quetelet, etc. The normal distribution can be used as an approximation to other distributions because the standardized sum of a large number of independent and identically distributed random variables is approximately normally distributed. Thus, the normal distribution can be used when a large number of non-normal distribution correspond more closely to observed values. The 1816 work of Gauss (Gauss 1816) is the earliest result...

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Normal Distribution, Univariate. Figure 1
Normal Distribution, Univariate. Figure 2

References and Further Reading

  • De Moivre A (1733) Approximatio ad Summam Ferminorum Binomii \({(\textrm{ a} + \textrm{ b})}^{\textrm{ n}}\) in Seriem expansi. Supplementum II to Miscellanae Analytica, pp 1–7

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  • Gauss CF (1816) Bestimmung der Genauigkeit der Beobachtungen. Z Astronom 1:185–197

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Rathie, P.N. (2011). Normal Distribution, Univariate. In: Lovric, M. (eds) International Encyclopedia of Statistical Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04898-2_425

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