pymc.TruncatedNormal

class pymc.TruncatedNormal(name, *args, rng=None, dims=None, initval=None, observed=None, total_size=None, transform=UNSET, default_transform=UNSET, **kwargs)

Univariate truncated normal log-likelihood.

The pdf of this distribution is

\[f(x;\mu ,\sigma ,a,b)={\frac {\phi ({\frac {x-\mu }{\sigma }})}{ \sigma \left(\Phi ({\frac {b-\mu }{\sigma }})-\Phi ({\frac {a-\mu }{\sigma }})\right)}}\]

Truncated normal distribution can be parameterized either in terms of precision or standard deviation. The link between the two parametrizations is given by

\[\tau = \dfrac{1}{\sigma^2}\]

(Source code, png, hires.png, pdf)

Support	\(x \in [a, b]\)
Mean	\(\mu +{\frac {\phi (\alpha )-\phi (\beta )}{Z}}\sigma\)
Variance	\(\sigma ^{2}\left[1+{\frac {\alpha \phi (\alpha )-\beta \phi (\beta )}{Z}}-\left({\frac {\phi (\alpha )-\phi (\beta )}{Z}}\right)^{2}\right]\)

Parameters:

mutensor_like of float, default 0

Mean.

sigmatensor_like of float, optional

Standard deviation (sigma > 0) (only required if tau is not specified). Defaults to 1 if neither sigma nor tau is specified.

tautensor_like of float, optional

Precision (tau > 0) (only required if sigma is not specified).

lowertensor_like of float, default - numpy.inf

Left bound.

uppertensor_like of float, default numpy.inf

Right bound.

Examples

with pm.Model():
    x = pm.TruncatedNormal("x", mu=0, sigma=10, lower=0)

with pm.Model():
    x = pm.TruncatedNormal("x", mu=0, sigma=10, upper=1)

with pm.Model():
    x = pm.TruncatedNormal("x", mu=0, sigma=10, lower=0, upper=1)

Methods

TruncatedNormal.dist([mu, sigma, tau, ...])

Create a tensor variable corresponding to the cls distribution.