Updated: 31 July 2010

Use FPDF to calculate the probability density function of the F distribution.

The probability density function is:

SELECT [wctStatistics].[wct].[FPDF] (

<@X, float,>

,<@Degrees_freedom1, float,>

,<@Degrees_freedom2, float,>)

is any real number. *@X *is an expression of type **float** or of a type that implicitly converts to **float**.

is the degrees of freedom. *@Degrees_freedom1 *is an expression of type **float** or of a type that implicitly converts to **float**.

is the degrees of freedom. *@Degrees_freedom2 *is an expression of type **float** or of a type that implicitly converts to **float**.

float

· *@Degrees_freedom1* must be greater than zero (*@Degrees_freedom1* > 0).

· *@Degrees_freedom2* must be greater than zero (*@Degrees_freedom2* > 0).

· *@X* must be greater than or equal to zero (*@X* ≥ zero).

· If *@X* = 0 and *@Degrees_freedom1* = 1 and *@Degrees_freedom2* =1 then FPDF is equal to infinity

SELECT wct.FPDF(1,2,1)

This produces the following result

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

0.192450089729876

(1 row(s) affected)

You can use the SeriesFloat function from the XLeratorDB/math library to generate a dataset which can be pasted into EXCEL to generate a graph of the function.

SELECT SeriesValue

,wct.FPDF(SeriesValue, 1, 1) as [f(x,1,1)]

,wct.FPDF(SeriesValue, 2, 1) as [f(x,2,1)]

,wct.FPDF(SeriesValue, 5, 2) as [f(x,5,2)]

,wct.FPDF(SeriesValue, 100, 1) as [f(x,100,1)]

,wct.FPDF(SeriesValue, 100, 100) as [f(x,100,100)]

FROM wct.SeriesFloat(0.1,8,.1,NULL,NULL)

This is an EXCEL-generated graph of the results