SQL Server T_DIST_2T Function

Updated 2023-11-05 12:20:05.027000

Description

Use the scalar function T_DIST_2T to calculate the two-tailed cumulative probability distribution of Student's t-distribution.

Syntax

SELECT [westclintech].[wct].[T_DIST_2T](
  <@X, float,>
 ,<@df, float,>)

Arguments

@X

the value of interest to be evaluated. @X must be of a type float or of type that intrinsically converts to float.

@df

the number of degrees of freedom. @df must of a type float or of a type that intrinsically converts to float.

Return Type

float

Remarks

0 < @df.

Examples

In this example we calculate the two-tailed cumulative distribution function for x = 60 with 1 degree of freedom.

SELECT wct.T_DIST_2T(   60, --@X
                        1   --@df
                    ) as T_DIST_2T;

This produces the following result.

T_DIST_2T
0.0106093472652465

The two-tailed cumulative distribution is closely related to the beta distribution.

SELECT wct.T_DIST_2T(x, df) as T_DIST_2T,
       1 - wct.BETA_DIST(x * x / (df + x * X), 0.5, df * 0.5, 'True', NULL, NULL)
                 as BETA_DIST
FROM
(
    VALUES
        (-2e-00, 5e-00)
) n (x, df);