Updated: 31 July 2010

Use CHI2NC to calculate the lower cumulative distribution function of the non-central chi-square distribution.

The probability density function is:

The lower cumulative distribution function is:

SELECT [wctStatistics].[wct].[CHI2NC] (

<@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.CHI2NC(1,3,3)

This produces the following result

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

0.0582469145317944

(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.CHI2NC(SeriesValue, 2, 1) as [f(x,2,1)]

,wct.CHI2NC(SeriesValue, 2, 2) as [f(x,2,2)]

,wct.CHI2NC(SeriesValue, 2, 3) as [f(x,2,3)]

,wct.CHI2NC(SeriesValue, 4, 1) as [f(x,4,1)]

,wct.CHI2NC(SeriesValue, 4, 2) as [f(x,4,2)]

,wct.CHI2NC(SeriesValue, 4, 3) as [f(x,4,3)]

FROM wct.SeriesFloat(0,8,.1,NULL,NULL)

This is an EXCEL-generated graph of the results