Normal/Gaussian Probability Distribution Family
(Redirected from normal distribution)
A Normal/Gaussian Probability Distribution Family is an exponential probability distribution family whose exponential function is of the form [math]f(x,a,b,c)[/math] (where [math]a = \tfrac{1}{\sqrt{2\pi\sigma^2}}[/math], [math]b = \mu[/math], and [math]c = 2\sigma^2[/math].
- AKA: [math]\mathcal{N}(x | \mu, \sigma)[/math]
- Context:
- It can be instantiated as a Gaussian Probability Density Function (or a Gaussian dataset), such as a standard Gaussian [math]\mathcal{N}(x | \mu=0, \sigma=1)[/math].
- It can range from being a Univariate Gaussian Distribution to being a Multivariate Gaussian Distribution.
- It can be a member of a Gaussian Mixture Model.
- …
- Counter-Example(s):
- See: Binomial Statistical Model, Multinomial Distribution.
References
2013
- http://en.wikipedia.org/wiki/Normal_distribution#Operations_on_normal_deviates
- The family of normal distributions is closed under linear transformations. That is, if X is normally distributed with mean μ and deviation σ, then the variable Y = aX + b, for any real numbers a and b, is also normally distributed, with mean aμ + b and deviation aσ.
