Beta
Bounded prior family on the unit interval in its standard form.
Parameters
| Argument | Symbol | Meaning | Default |
|---|---|---|---|
a |
\(\alpha\) | First shape parameter | 1.0 |
b |
\(\beta\) | Second shape parameter | 1.0 |
random_state |
- | RNG seed / generator | None |
Implementation Parameterization
The implementation uses the canonical beta family on [0, 1].
The API only accepts the two shape parameters a and b;
arbitrary low / high interval scaling is not part of this distribution class.
\[
f(x;\alpha,\beta)=
\frac{\Gamma(\alpha+\beta)}{\Gamma(\alpha)\Gamma(\beta)}
x^{\alpha-1}(1-x)^{\beta-1}
\]
Region
\[
x \in [0,1]
\]