Normal Distribution
Normal Distribution Definition
The normal distributions are a very important class of statistical distributions. All normal distributions are symmetric and have bell-shaped density curves with a single peak. A function that represents the distribution of many random variables as a symmetrical bell-shaped graph.
A normal distribution in a variate 
with mean 
and variance 
is a statistic distribution with probability
density function
 |
(1)
|
. While statisticians
and mathematicians uniformly use the term "normal distribution" for this
distribution, physicists sometimes call it a Gaussian distribution and, because of
its curved flaring shape, social scientists refer to it as the "bell curve."
Feller (1968) uses the symbol 
for 
in the above equation, but then switches to
in Feller (1971).
de Moivre developed the normal distribution as an approximation to the binomial distribution, and it was subsequently used by Laplace in 1783 to study measurement errors and by Gauss in 1809 in the analysis of astronomical data (Havil 2003, p. 157).
