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CHISQPDF

Updated 2024-03-07 21:16:40.027000

Syntax

SELECT [westclintech].[wct].[CHISQPDF] (
  <@X, float,>
 ,<@Degrees_freedom, float,>)

Description

Use the scalar function CHISQPDF to calculate the probability density function of the chi square distribution.

The probability density function is:

f\left(x,v\right)=\frac{x^{v^2-1}e^{-\frac{x}{2}}}{2^\frac{v}{2}\Gamma\left(\frac{v}{2}\right)}

Arguments

@Degrees_Freedom

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

@X

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

Return Type

float

Remarks

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

Examples

SELECT wct.CHISQPDF(1, 3) as [CHISQ pdf];

This produces the following result.

{"columns":[{"field":"CHISQ pdf","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"}],"rows":[{"CHISQ pdf":"0.241970724519143"}]}

You can use the SreiesFloat 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.CHISQPDF(SeriesValue, 1) as [f(x,1)],

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

       wct.CHISQPDF(SeriesValue, 4) as [f(x,5)],

       wct.CHISQPDF(SeriesValue, 7) as [f(x,7)],

       wct.CHISQPDF(SeriesValue, 9) as [f(x,9)]

FROM wct.SeriesFloat(0.1, 20, .1, NULL, NULL);

This is an EXCEL-generated graph of the results

http://westclintech.com/Portals/0/images/doc_stats_CHISQPDF_img1.jpg