Continuous Attributes and Distributions

• Normal Distribution (Gaussian).
• Normal + Fisher.
• Student's t-Distribution.
• von Mises - Fisher, directions in R^D, and von Mises, angular (circular, cyclic, periodic) attributes, where D = 2.
• 1-D linear regression, y = a*x+b+N(0,σ), and polynomial-fitting.

This section and its sub-pages are about continuous probability distributions such as the normal distribution (Gaussian distribution), and estimating the parameters of such distributions from given data.

For example, the probability density function (pdf) of a normal distribution, N(μ, σ), with mean μ and standard deviation σ > 0, for -∞ < x < ∞, is:

f(x) = (1 / √(2π).σ) . e^{-(x-μ)2 / 2σ2}

 

Note that f(x) is symmetric about x=μ, and it is the case, of course, that

 

_-∞∫^+∞ f(x) dx = 1