Updated: 31 July 2010

Use NCTPDF to calculate the probability density function of the non-central T distribution.

The formula for the probability density function is:

SELECT [wctStatistics].[wct].[NCTPDF] (

<@X, float,>

,<@DF, float,>

,<@Lambda, float,>)

is the variable to be evaluated. @*X *is an expression of type **float** or of a type that implicitly converts to **float**.

degrees of freedom. @*DF *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

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

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

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

Calculate the probability density function:

SELECT wct.NCTPDF(1,3,3)

This produces the following result

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

0.0700404713849545

(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 porbability density function.

SELECT SeriesValue

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

,wct.NCTPDF(SeriesValue, 3, 1) as [f(x,3,1)]

,wct.NCTPDF(SeriesValue, 5, 1) as [f(x,5,1)]

,wct.NCTPDF(SeriesValue, 1, 3) as [f(x,1,3)]

,wct.NCTPDF(SeriesValue, 1, 5) as [f(x,1,5)]

FROM wctMath.wct.SeriesFloat(.1, 10, .1,NULL,NULL)

This is an EXCEL-generated graph of the results