InvGamma
Inverse-gamma prior family.
Parameters
| Argument | Symbol | Meaning | Default |
|---|---|---|---|
mean |
\(\mu\) | Mean of the inverse-gamma prior | 1.0 |
std |
\(\sigma\) | Standard deviation of the inverse-gamma prior | 1.0 |
random_state |
- | RNG seed / generator | None |
Implementation Parameterization
The implementation derives the canonical inverse-gamma parameters \alpha and \beta from mean and std:
alpha = 2 + (mean / std) ** 2 and
beta = mean * (alpha - 1).
The public API does not expose separate loc / scale wrapper parameters.
\[
f(x;\alpha,\beta)=
\frac{\beta^\alpha}{\Gamma(\alpha)}
x^{-(\alpha+1)}
\exp\left(-\frac{\beta}{x}\right)
\]
Region
\[
x \in (0,\infty)
\]