StatsStudentCDF

StatsStudentCDF (t, n)

The StatsStudentCDF function returns the Student (uniform) cumulative distribution function.

F(t, n)=\left\{\begin{array}{ll} \displaystyle \frac{1}{2}\left\{1+I\left(\frac{n}{2}, \frac{1}{2} ; 1\right)-I\left(\frac{n}{2}, \frac{1}{2} ; \frac{n}{n+t^{2}}\right)\right\} & t>0 \\ \\ \displaystyle \frac{1}{2}\left\{1+I\left(\frac{n}{2}, \frac{1}{2} ; \frac{n}{n+t^{2}}\right)-I\left(\frac{n}{2}, \frac{1}{2} ; 1\right)\right\} & t<0 \\ \\ \displaystyle \frac{1}{2} & t=0 . \end{array}\right.

where n >0 is the degrees of freedom and is the incomplete beta function betai.