3.5.3.3.17 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. \(0<p<1\)

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.