F_INV

Updated 2023-11-02 21:44:11.583000

Syntax

SELECT [westclintech].[wct].[F_INV](
  <@p, float,>
 ,<@df1, float,>
 ,<@df2, float,>)

Description

Use the scalar function F_INV to calculate the inverse of the F lower probability distribution.

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.

{"columns":[{"field":"F_INV","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"}],"rows":[{"F_INV":"19.2964096520172"}]}

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);