/math-44ee9fb60a9f10b64773550e0f8ffd5c.png "tp = tinv(p, df)")
computes the deviate associated with the lower tail probability of Student's t-distribution with real degrees of freedom. computes the deviate associated with the lower tail probability of Student's t-distribution with real degrees of freedom.
The deviate,/math-5c2423d9bb6800593fddead13d1534d3.png "t_p")
associated with the lower tail probability,/math-d85cbe02cc02e5eb719efacb6e2ed3a2.png "p")
, of the Student's t-distribution with /math-4fdefba26320686bb2bd0579a0df421c.png "\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](../images/Tinv_(function)/math-08463b6d65b20a8e21302c2da6f15889.png "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")
, /math-5d93f7fcbcdb950a9a7add4f7190c24d.png "\nu \geq 1")
/math-a2ce2d0e19ea7ec82c10e480f8475435.png "0<p<1")
, of the Student's t-distribution.(/math-dcba4d5e9eb96c31ae58de384bda0d28.png "df \geq 1")
)/math-e358efa489f58062f10dd7316b65649e.png "t")
variate.