Normal distribution

The normal distribution, also called Gaussian distribution, is an extremely important probability distribution in many fields.

History

The normal distribution was first introduced by de Moivre in an article in 1733 (reprinted in the second edition of his The Doctrine of Chances, 1738) in the context of approximating certain binomial distributions for large n. His result was extended by Laplace in his book Analytical Theory of Probabilities (1812), and is now called the Theorem of de Moivre-Laplace.

Related Topics:
De Moivre - 1733 - The Doctrine of Chances - 1738 - Binomial distribution - Laplace - Analytical Theory of Probabilities - 1812 - Theorem of de Moivre-Laplace

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Laplace used the normal distribution in the analysis of errors of experiments. The important method of least squares was introduced by Legendre in 1805. Gauss, who claimed to have used the method since 1794, justified it rigorously in 1809 by assuming a normal distribution of the errors.

Related Topics:
Analysis of errors - Method of least squares - Legendre - 1805 - Gauss - 1794 - 1809

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

The name "bell curve" goes back to Jouffret who used the term "bell surface" in 1872 for a bivariate normal with independent components. The name "normal distribution" was coined independently by Charles S. Peirce, Francis Galton and Wilhelm Lexis around 1875. This terminology is unfortunate, since it reflects and encourages the fallacy that many or all probability distributions are "normal". (See the discussion of "occurrence" below.)

Related Topics:
Jouffret - 1872 - Bivariate normal - Charles S. Peirce - Francis Galton - Wilhelm Lexis - 1875

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

That the distribution is called the normal or Gaussian distribution is an instance of Stigler's law of eponymy:

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

"No scientific discovery is named after its original discoverer."

~ ~ ~ ~ ~ ~ ~ ~ ~ ~