Gamma
Positive prior family parameterized by mean and standard deviation.
Parameters
| Argument | Symbol | Meaning | Default |
|---|---|---|---|
mean |
\(\mu\) | Mean of the gamma random variable | 1.0 |
std |
\(\sigma\) | Standard deviation of the gamma random variable | 1.0 |
random_state |
- | RNG seed / generator | None |
Implementation Parameterization
The implementation converts (mean, std) into the gamma parameters k and \theta:
\[
k=\left(\frac{\mu}{\sigma}\right)^2,\quad
\theta=\frac{\sigma^2}{\mu}
\]
These parameters are then used directly in the density and sampler.
The public API does not expose separate loc / scale wrapper parameters.
\[
f(x;k,\theta)=
\frac{1}{\Gamma(k)\theta^k}
x^{k-1}e^{-x/\theta}
\]
Region
\[
x \in [0,\infty)
\]