3.5.3.3.15 Tinv

Definition:

$tp = tinv(p, df)$ computes the deviate associated with the lower tail probability of Student's t-distribution with real degrees of freedom.

The deviate,$t_p$ associated with the lower tail probability,$p$, of the Student's t-distribution with $\nu$ degrees of freedom is defined as the solution to

$P(T\leq t_p)=\frac{\Gamma ((\nu +1)/2)}{\sqrt{\pi \nu }\Gamma (\nu /2)}\int_{-\infty }^{t_p}[1+\frac{T^2}\nu ]^{-(\nu +1)/2}dT$ , $\nu \geq 1$

Parameters:

p (input, double)
The probability. $0
df (input, double)
The degrees of freedom, $\nu$ , of the Student's t-distribution.($df \geq 1$)
tp (output, double)
The value of the Student's $t$ variate.