Student’s T

class stats_arrays.StudentsTUncertainty

Bases: stats_arrays.distributions.base.UncertaintyBase

The Student’s T uncertainty distribution probability density function is a function of \(\nu\), the degrees of freedom:

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

A non-standardized distribution, with a location and scale parameter, is also possible, through the transformation:

\[X = \mu + \sigma f\]

In our implementation, the location parameter \(\mu\) is location, the scale parameter \(\sigma\) is scale, and \(\nu\) (the degrees of freedom) is shape.