atoti.stats.t.pdf()#

atoti.stats.t.pdf(point, /, *, degrees_of_freedom)#

Probability density function for a Student’s t distribution.

Warning

This feature is experimental, its key is "stats.t.pdf".

The pdf of a Student’s t-distribution is:

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

where \(\nu\) is the number of degrees of freedom and \(\Gamma\) is the gamma function.

Parameters:

point (VariableMeasureConvertible) – The point where the function is evaluated.
degrees_of_freedom (StrictlyPositiveNumber | VariableMeasureConvertible) – The number of degrees of freedom. Must be positive.

Return type:

MeasureDefinition