Uniform Distribution

#distribution #continuous_distribution

Gist

A continuous distribution that assumes equal probability across all values.

Mathematics

f_{X} (x) = {\begin{cases} \frac{1}{b - a}, & a < x < b, \\ 0, & x < a o r x > b, \end{cases}

Properties

Mean: $\frac{a + b}{2}$
Variance: $\frac{(b - a)^{2}}{12}$

Usage

Can be used for a very weak Prior in Bayesian analysis. Though be careful it can be an illusion of being uninformative!

Code

R