The beta distribution
The parameters are \(\alpha,\beta>0\), and \(A,B\) with \(B\ge A\).
For \(A\le x\le B\)
When \(A=0,B=1\), it is called the standard Beta distribution.
Essentially, \(A,B\) are used to stretch/shift the curve. It is defined only for values between \(A\) and \(B\).
It is often used to model the proportion of percentage of a quantity in different samples (e.g. % of 24-hour day an individual is asleep).