F_DIST_RT

Updated 2023-11-02 21:41:46.130000

Syntax

SELECT [westclintech].[wct].[F_DIST_RT](
  <@x, float,>
 ,<@df1, float,>
 ,<@df2, float,>)

Description

Use the scalar function F_DIST_RT to calculate upper cumulative probability of an F-distribution for x and degrees of freedom for 2 independent random variables.

Arguments

@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.

@X

The value of interest to be evaluated. @X must be of a type float or of 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 < @X.

0 < @df1.

0 < @df2.

Examples

In this example we calculate the F cumulative distribution function for x = 9 with 4 numerator degrees of freedom and 5 denominator degrees of freedom.

SELECT wct.F_DIST_RT(   9, --@x

                        4, --@df1

                        5  --@df2

                    ) as F_DIST_RT;

This produces the following result.

{"columns":[{"field":"F_DIST_RT","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"}],"rows":[{"F_DIST_RT":"0.0165940658046558"}]}

The F distribution is closely related to the beta distribution.

SELECT wct.F_DIST_RT(x, df1, df2) as F_DIST_RT,

       wct.BETA_DIST(df2 / (df2 + df1 * x), df2 / 2, df1 / 2, 'True', NULL, NULL)

                 as BETA_DIST

FROM

(

    VALUES

        (0.95, 6e-00, 11e-00)

) n (x, df1, df2);