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


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.