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.

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Inverse of Cumulative Distribution Functions (INV)

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