Updated: 31 July 2010

Use NCFCDF to calculate the inverse of the lower cumulative distribution function of the non-central F distribution.

The formula for the lower cumulative density function is:

SELECT [wctStatistics].[wct].[NCFINV] (

<@CDF, float,>

,<@DF1, float,>

,<@DF2, float,>

,<@Lambda, float,>)

is cumulative distribution function. @*CDF *is an expression of type **float** or of a type that implicitly converts to **float**.

degrees of freedom. @*DF1 *is an expression of type **float** or of a type that implicitly converts to **float**.

degrees of freedom. @*DF2 *is an expression of type **float** or of a type that implicitly converts to **float**.

is the non-centrality parameter. @*Lambda *is an expression of type **float** or of a type that implicitly converts to **float**.

float

· *@CDF* must be greater than zero and less than one (0* < @CDF* < 1).

· *@DF1* must be greater than zero (*@DF1* > 0).

· *@DF2* must be greater than zero (*@DF2* > 0).

· *@Lambda* must be greater than or equal to zero (*@Lambda* > 0).

Calculate the lower cumultive distribution function:

SELECT wct.NCFCDF(0.5,3,2,1)

This produces the following result

----------------------

0.210838872156613

(1 row(s) affected)

Calculate the inverse:

SELECT wct.NCFINV(0.210838872156613,3,2,1)

This produces the following result

----------------------

0.5

(1 row(s) affected)