TruncNormal
Continuous normal prior truncated to a finite interval.
Parameters
| Argument | Symbol | Meaning | Default |
|---|---|---|---|
low |
\(\ell\) | Lower truncation bound | -6.0 |
high |
\(h\) | Upper truncation bound | 6.0 |
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
This is a true truncated normal on the closed interval [low, high].
The density is the underlying normal renormalized over that interval;
the implementation does not use clipped or censored point masses at the bounds.
\[
f(x;\mu,\sigma,\ell,h)=
\frac{\phi\!\left(\frac{x-\mu}{\sigma}\right)}
{\sigma\left[\Phi\!\left(\frac{h-\mu}{\sigma}\right)-\Phi\!\left(\frac{\ell-\mu}{\sigma}\right)\right]}
\]
Region
\[
x \in [\ell,h]
\]