TI-BASIC:Invt - Revision history

Maintenance script: Automated @@ correction

2016-02-24T22:12:10Z

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	{{Template:TI-BASIC:Command		{{Template:TI-BASIC:Command
	\|picture=@@		\|picture=
	\|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'')

KermMartian at 19:24, 24 February 2016

2016-02-24T19:24:03Z

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

	~~[[TI-BASIC:Math\|Math]]~~		<math>
	\definecolor{darkgreen}{rgb}{0.90,0.91,0.859}\pagecolor{darkgreen}		\definecolor{darkgreen}{rgb}{0.90,0.91,0.859}\pagecolor{darkgreen}
	\operatorname{invT}(p,1)=\tan\left(\pi\left(p-\frac1{2}\right)\right)		\operatorname{invT}(p,1)=\tan\left(\pi\left(p-\frac1{2}\right)\right)
	~~[[TI-BASIC:~~/math~~\|/math]]~~		</math>

	= Related Commands =		= Related Commands =

Maintenance script: Initial automated import

2016-02-24T18:33:31Z

Initial automated import

New page

{{Template:TI-BASIC:Command
|picture=@@
|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'')
|location=Press:
# 2ND DISTR to access the distribution menu
# 4 to select invT(, or use arrows.
|compatibility=TI-84+/SE (OS 2.30 or greater)
|size=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 [[TI-BASIC:Tpdf|Tpdf(]] and [[TI-BASIC:Tcdf|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:

[[TI-BASIC:Math|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)
[[TI-BASIC:/math|/math]]

= Related Commands =

* [[TI-BASIC:Tpdf|Tpdf(]]
* [[TI-BASIC:Tcdf|Tcdf(]]
* [[TI-BASIC:Shade_T|Shade_T(]][[Category:TI-BASIC]]
[[Category:TIBD]]