pymc.StudentT

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

Student’s T log-likelihood.

Describes a normal variable whose precision is gamma distributed. If only nu parameter is passed, this specifies a standard (central) Student’s T.

The pdf of this distribution is

\[f(x|\mu,\lambda,\nu) = \frac{\Gamma(\frac{\nu + 1}{2})}{\Gamma(\frac{\nu}{2})} \left(\frac{\lambda}{\pi\nu}\right)^{\frac{1}{2}} \left[1+\frac{\lambda(x-\mu)^2}{\nu}\right]^{-\frac{\nu+1}{2}}\]

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

Support

\(x \in \mathbb{R}\)

Parameters:

nutensor_like of float

Degrees of freedom, also known as normality parameter (nu > 0).

mutensor_like of float, default 0

Location parameter.

sigmatensor_like of float, optional

Scale parameter (sigma > 0). Converges to the standard deviation as nu increases (only required if lam is not specified). Defaults to 1.

lamtensor_like of float, optional

Scale parameter (lam > 0). Converges to the precision as nu increases (only required if sigma is not specified). Defaults to 1.

Examples

with pm.Model():
    x = pm.StudentT("x", nu=15, mu=0, sigma=10)

with pm.Model():
    x = pm.StudentT("x", nu=15, mu=0, lam=1 / 23)

Methods

StudentT.dist(nu[, mu, sigma, lam])

Create a tensor variable corresponding to the cls distribution.