# pymc.SkewStudentT#

class pymc.SkewStudentT(name, *args, rng=None, dims=None, initval=None, observed=None, total_size=None, transform=UNSET, default_transform=UNSET, **kwargs)[source]#

Skewed Student’s T distribution log-likelihood.

This follows Jones and Faddy (2003)

The pdf of this distribution is

$f(t)=f(t ; a, b)=C_{a, b}^{-1}\left\{1+\frac{t}{\left(a+b+t^2\right)^{1 / 2}}\right\}^{a+1 / 2}\left\{1-\frac{t}{\left(a+b+t^2\right)^{1 / 2}}\right\}^{b+1 / 2}$

where

$C_{a, b}=2^{a+b-1} B(a, b)(a+b)^{1 / 2}$
 Support $$x \in [\infty, \infty)$$ Mean $$E(T)=\frac{(a-b) \sqrt{(a+b)}}{2} \frac{\Gamma\left(a-\frac{1}{2}\right) \Gamma\left(b-\frac{1}{2}\right)}{\Gamma(a) \Gamma(b)}$$
Parameters:
a

First kurtosis parameter (a > 0).

b

Second kurtosis parameter (b > 0).

mu

Location parameter.

sigma

Scale parameter (sigma > 0). Converges to the standard deviation as a and b become close (only required if lam is not specified). Defaults to 1.

lamtensor_like of float, optional

Scale parameter (lam > 0). Converges to the precision as a and b become close (only required if sigma is not specified). Defaults to 1.

Methods

 SkewStudentT.dist(a, b, *[, mu, sigma, lam]) Creates a tensor variable corresponding to the cls distribution.