Updated: 31 July 2010

Use NCHISQPDF to calculate the probability density function of the non-central chi square distribution.

The probability density function is:

SELECT [wctStatistics].[wct].[NCHISQPDF] (

<@X, float,>

,<@DF, float,>

,<@Lambda, 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. *@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

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

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

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

SELECT wct.NCHISQPDF(1,3,1)

This produces the following result

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

0.172475656944122

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

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

,wct.NCHISQPDF(SeriesValue, 3, 5) as [f(x,3,5)]

,wct.NCHISQPDF(SeriesValue, 10, 1) as [f(x,10,1)]

,wct.NCHISQPDF(SeriesValue, 10, 3) as [f(x,10,3)]

,wct.NCHISQPDF(SeriesValue, 10, 5) as [f(x,10,5)]

FROM wct.SeriesFloat(0.0,20,.1,NULL,NULL)

This is an EXCEL-generated graph of the results