Student’s T¶
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class
stats_arrays.StudentsTUncertainty¶ Bases:
stats_arrays.distributions.base.UncertaintyBaseThe 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 \(\sigma\) isscale, and \(\nu\) (the degrees of freedom) isshape.