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The invT( Command

Command Summary Command Syntax Calculator Compatibility Token Size
Calculates the inverse of the cumulative Student's t-distribution function with degrees of freedom ν. invT(probability, ν) TI-84+/SE (OS 2.30 or greater) 2 bytes

Press:
1. 2ND DISTR to access the distribution menu
2. 4 to select invT(, or use arrows.

The invT( Command

invT( is the inverse of the cumulative Student t distribution function: given a probability p and a specified degrees of freedom v, it will return the number x such that tcdf(E-99,*x*,*v*) is equal to p

:invT(.95,24
    1.710882023

Advanced

invT( is meant for use with so-called "one-tailed' tests; for two-tailed tests, the proper expression to use (corresponding to the inverse of tcdf(-*x*,*x*,*v*)) is invT(.5(1+*p*),*v*)

Formulas

Unlike the tpdf( and tcdf( commands, the invT( command does not have a closed-form formula. However, it can be expressed in terms of the inverse incomplete beta function.

For one degree of freedom, invT( is expressible in terms of simpler functions:

\[\operatorname{invT}(p,1)=\tan\left(\pi\left(p-\frac1{2}\right)\right)\]
Authors: KG