tinv

Student's t inverse cumulative distribution function

Syntax

x = tinv(p,nu)

Description

x = tinv(p,nu) returns the inverse of Student's t cdf using the degrees of freedom in nu for the corresponding probabilities in p. p and nu can be vectors, matrices, or multidimensional arrays that are the same size. A scalar input is expanded to a constant array with the same dimensions as the other inputs. The values in p must lie on the interval [0 1].

The t inverse function in terms of the t cdf is

x=F1(p|ν)={x:F(x|ν)=p}

where

p=F(x|ν)=xΓ(ν+12)Γ(ν2)1νπ1(1+t2ν)ν+12dt

The result, x, is the solution of the cdf integral with parameter ν, where you supply the desired probability p.

Examples

expand all

Compute Student's t icdf

What is the 99th percentile of the Student's t distribution for one to six degrees of freedom?

percentile = tinv(0.99,1:6)
percentile =

   31.8205    6.9646    4.5407    3.7469    3.3649    3.1427

See Also

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