 # SQL Server F.INV.RT function

F_INV_RT

Updated: 31 July 2015

Use F_INV_RT to calculate the inverse of the F upper probability distribution.
Syntax
SELECT [wct].[F_INV_RT](
<@p, float,>
,<@df1, float,>
,<@df2, float,>)
Arguments
@p
The quantile of interest to be evaluated. @X must be of a type float or of type that intrinsically converts to float
@df1
The number of degrees freedom for the numerator random variable. @df1 must be of a type float or of a type that intrinsically converts to float.
@df2
The number of degrees freedom for the denominator random variable. @df2 must be of a type float or of a type that intrinsically converts to float.
Return Type
float
Remarks
·         0 < @p < 1
·         0 < @df1
·         0 < @df2
Examples
In this example we calculate the inverse of the right-tailed F distribution with (5,2) degrees of freedom at 0.05.
SELECT
wct.F_INV_RT(
0.05  --@p
,5     --@df1
,2     --@df2
) as F_INV_RT

This produces the following result

The F distribution is closely related to the beta distribution.
SELECT
wct.F_INV_RT(p,df1,df2) as F_INV_RT
,(df2*(1-wct.BETAINV(p,df2/2,df1/2,NULL,NULL)))/(wct.BETAINV(p,df2/2,df1/2,NULL,NULL)* df1) as BETAINV
FROM (
VALUES (0.05,5e-00,2e-00))n(p,df1,df2)

This produces the following result.

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