Commonly used distributions defined with support $[0,1]$

Question

Help name some commonly used distributions defined over $[0,1]$ (i.e. support $[0,1]$), for example, uniform distribution over $[0,1]$, beta distribution. Any others?

Answer 1

Triangular distribution on $[0,1]$, trapezoidal distribution on $[0,1]$ truncated normal distribution on $[0,1]$,...

These are not commonly used as far as I know, but most other commonly used distributions of these form are a special case of the beta distribution.

See this wikipedia link for more of them.