Normal Distribution

  Also called a Gaussian distribution, this is in practice one of the most important distributions, since experimental errors are often normally distributed to a good approximation ( Central Limit Theorem), and, further, the normal assumption simplifies many theorems and methods of data analysis (e.g. the method of least squares).

The normal distribution has the following properties:

It has two parameters, the mean a and the width , which can be estimated from a sample by the following estimators:

In the statistical literature the probability density function of the normal distribution is often denoted by ). The standard normal distribution has zero mean and unit variance, i.e.

The corresponding distribution function is denoted by

This is the complement of what is usually denoted as error function (the name is also used in other contexts), i.e. .