 # SQL Server F.INV function

F_INV

Updated: 31 July 2015

Use F_INV to calculate the inverse of the F lower probability distribution.
Syntax
SELECT [wct].[F_INV](
<@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 F distribution with (5,2) degrees of freedom at 0.95.
SELECT
wct.F_INV(
0.95         --@p
,5            --@df1
,2            --@df2
) as F_INV

This produces the following result

The F distribution is closely related to the beta distribution.
SELECT
wct.F_INV(p,df1,df2) as F_INV
,df2*wct.BETAINV(p,df1/2,df2/2,NULL,NULL)/(df1*(1-wct.BETAINV(p,df1/2,df2/2,NULL,NULL))) as BETAINV
FROM (
VALUES (0.95,5e-00,2e-00))n(p,df1,df2)

This produces the following result.

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