LogNormal
Canonical lognormal prior family on positive support.
Parameters
| Argument | Symbol | Meaning | Default |
|---|---|---|---|
mean |
\(\mu\) | Mean of the underlying normal distribution | 0.0 |
std |
\(\sigma\) | Standard deviation of the underlying normal distribution | 1.0 |
random_state |
- | RNG seed / generator | None |
Implementation Parameterization
The API takes the underlying normal parameters directly:
X = exp(N(mean, std**2)).
No additional shift or scale wrapper parameters are exposed.
\[
f(x;\mu,\sigma) =
\frac{1}{x\sigma\sqrt{2\pi}}
\exp\left(-\frac{(\log x-\mu)^2}{2\sigma^2}\right)
\]
Region
\[
x \in (0,\infty)
\]