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:
- atensor_like of
float First kurtosis parameter (a > 0).
- btensor_like of
float Second kurtosis parameter (b > 0).
- mutensor_like of
float Location parameter.
- sigmatensor_like of
float 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.
- atensor_like of
Methods
SkewStudentT.dist(a, b, *[, mu, sigma, lam])Creates a tensor variable corresponding to the cls distribution.