Normal
Overview
The normal distribution is the standard probability distribution known as the Guassian, or the bell curve.
It is one or the most common distributions used in statistical modeling, usually because of its use in the
central limit theorem.
The normal distribution exhibits a characteristic bell shape.
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Formal Definition
The normal density function is given by
{% f(x) = \sqrt{1/2\pi \sigma^2 } \times e ^{-0.5 [(x-\mu)/\sigma]^2} %}
For multivariable distributions
{% f(\vec{x}| \vec{\mu}, \Sigma) = \frac{1}{(2\pi )^{D/2} | \Sigma | ^{1/2}} exp[-\frac{1}{2} (\vec{x} - \vec{\mu})^T \Sigma ^{-1} (\vec{x} - \vec{\mu}) ] %}
Properties
Library
A library for calculating normal distributions can be found at
normal library
