Gaussian Density Function Structure

A Gaussian Density Function Structure is a probability density function structure from a Gaussian probability distribution family (where [math]\displaystyle{ a = \tfrac{1}{\sqrt{2\pi\sigma^2}} }[/math], [math]\displaystyle{ b = \mu }[/math], and [math]\displaystyle{ c = 2\sigma^2 }[/math]).

AKA: Normal Distribution Structure.
Context:
- It can range from (typically) being a Univariate Gaussian Density Function to being a Multivariate Gaussian Density Function (such as a bivariate Gaussian function).
- It can (attempt to) represent a Gaussian Process (as a Gaussian random variable).
- It can be a Zero-Mean Gaussian Density Function.
- …
Example(s):
- a Standard Gaussian Density Function.
- a Univariate Normal Function, such as [math]\displaystyle{ \mathcal{N}(x | 1.1, 0.2) }[/math]
- a Bivariate Normal Function, such as:
Counter-Example(s):
- a Uniform Probability Function.
- a Non-Normal Distribution, such as a Poisson density function.
See: Gaussian Mixture Function, t-Student Distribution, Uniform Probability Distribution; Balanced Probability Distribution.

References

(Zhang, 2011c) ⇒ Xinhua Zhang. (2011). “Gaussian Distribution.” In: (Sammut & Webb, 2011) p.425

(Dubnicka, 2006h) ⇒ Suzanne R. Dubnicka. (2006). “The Normal Distribution and Related Distributions - Handout 8." Kansas State University, Introduction to Probability and Statistics I, STAT 510 - Fall 2006.
- TERMINOLOGY : A random variable X is said to have a normal distribution if its pdf is given by fX(x) = … 0, otherwise.
  Shorthand notation is X N(μ, 2). There are two parameters in the normal distribution: the mean μ and the variance 2.