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300px Probability density function of Gaussian distribution (bell curve).The normal distribution is an extremely important probability distribution in many fields.
It is also called the Gaussian distribution,
especially in physics and engineering.
It is actually a family of distributions of the same general form, differing only in their location and scale parameters: the mean and standard deviation. The standard normal distribution is the normal distribution with a mean of zero and a standard deviation of one. Because the graph of its probability density resembles a bell, it is often called the bell curve.
1 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.
Laplace used the normal distribution in the analysis of errors of experiments. The important method of least squares was introduced by Legendre in 1805Events January 11 Michigan Territory is created. February 15 Harmony Society officially formed March 1 Justice Samuel Chase acquitted of impeachment charges by the U. Senate April 27 United States Marines and Berbers attack the Tripolitan city of Derna (T. GaussJohann Carl Friedrich Gauss (Gauss ( April 30, 1777 February 23, 1855) was a legendary German mathematician, astronomer and physicist with a very wide range of contributions; he is considered to be one of the greatest mathematicians of all time. His name, who claimed to have used the method since 1794Events February 11 1st session of US Senate open to the public. March 14 Eli Whitney is granted a patent for the cotton gin. March 27 The United States Government established a permanent United States Navy and authorized the building of six vessels (in 17, justified it rigorously in 1809Events January 16 Peninsular War: The British defeat the French at the Battle of Corunna. February 3 Illinois Territory was created. February 11 Robert Fulton patents the steamboat. February 20 A decision by the Supreme Court of the United States states t by assuming a normal distribution of the errors.
The name "bell curve" goes back to Jouffret who used the term "bell surface" in 1872Events January 2 Brigham Young, is arrested for bigamy (25 wives). February 20 In New York City the Metropolitan Museum of Art opens. March 1 Yellowstone National Park is established as the world's first national park March 5 George Westinghouse patents t for a bivariate normalIn probability theory and statistics, a random vector X X . X follows a multivariate normal distribution also sometimes called a multivariate Gaussian distribution (in honor of Carl Friedrich Gauss, who was not the first to write about the normal distribu with independent components. The name "normal distribution" was coined independently by Charles S. Peirce, Francis Galton and Wilhelm Lexis around 1875 [Stigler]. 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).
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".
