Difference between revisions of "TI-BASIC:Invt"
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|summary=Calculates the inverse of the cumulative [*https://en.wikipedia.org/wiki/Student%27s_t-distribution Student's t-distribution] function with degrees of freedom ν. | |summary=Calculates the inverse of the cumulative [*https://en.wikipedia.org/wiki/Student%27s_t-distribution Student's t-distribution] function with degrees of freedom ν. | ||
|syntax=invT(''probability'', ''ν'') | |syntax=invT(''probability'', ''ν'') | ||
Latest revision as of 22:12, 24 February 2016
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Command Summary
Calculates the inverse of the cumulative [*https://en.wikipedia.org/wiki/Student%27s_t-distribution Student's t-distribution] function with degrees of freedom ν.
Command Syntax
invT(probability, ν)
Menu Location
Press:
- 2ND DISTR to access the distribution menu
- 4 to select invT(, or use arrows.
TI-84+/SE (OS 2.30 or greater)
2 bytes
invT( is the inverse of the cumulative Student t distribution function: given a probability p and a specified degrees of freedom ν, it will return the number x such that tcdf(-E99,x,ν) 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,ν)) is invT(.5(1+p),ν)
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:
<math> \definecolor{darkgreen}{rgb}{0.90,0.91,0.859}\pagecolor{darkgreen} \operatorname{invT}(p,1)=\tan\left(\pi\left(p-\frac1{2}\right)\right) </math>
