Normal distribution, also known as "normal distribution" and Gaussian distribution, was first obtained by de moivre in the asymptotic formula for finding binomial distribution. C.F. Gauss deduced it from another angle when studying the measurement error. Laplace and Gauss studied its properties. It is a very important probability distribution in mathematics, physics, engineering and other fields, and has great influence in many aspects of statistics.

The normal curve is bell-shaped, with low ends and high middle, which is symmetrical left and right, so people often call it bell-shaped curve.

If the random variable X obeys the normal distribution with a mathematical expectation of μ and a variance of σ 2, it is recorded as N(μ, σ 2). The expected value μ of probability density function with normal distribution determines its position, and its standard deviation σ determines its distribution amplitude. When μ = 0 and σ = 1, the normal distribution is standard normal distribution.

Chinese name

normal distribution

Foreign name

normal distribution

Another name

normal distribution

discoverer

De moivre ().

subject

probability theory

quick

navigate by water/air

Application of property distribution curve defined by theorem in studying process curve

Ethnicity

The concept of normal distribution was first put forward by German mathematician and astronomer De Moivre in 1733. However, because the German mathematician Gauss first applied it to astronomical research, it is also called Gaussian distribution. Gauss's work had a great influence on later generations. At the same time, he gave it the name of "Gaussian distribution", and the reason why later generations attributed the invention right of the least square method to him is also. However, today, the Gaussian head of 10 mark on German banknotes is also printed with a normal distribution density curve.