CHISQ_DIST
Updated 2023-11-02 21:06:18.793000
Syntax
SELECT [westclintech].[wct].[CHISQ_DIST](
<@X, float,>
,<@Degrees_freedom, float,>
,<@Cumulative, bit,>)
Description
Use the scalar function CHISQ_DIST to calculate the probability density or the lower cumulative probability of a chi-squared distribution for x and a number of degrees of freedom.
Arguments
@Cumulative
A bit value indicating whether the probability density function ( 'False') or the cumulative distribution function ( 'True') should be returned.
@X
The value of interest to be evaluated. @X must be of a type float or of type that intrinsically converts to float.
@Degrees_freedom
The number of degrees freedom. @Degrees_freedom must be of a type float or of a type that intrinsically converts to float.
Return Type
float
Remarks
0 < @X.
0 < @Degrees_freedom.
Examples
In this example we calculate the chi-squared lower-tailed cumulative distribution function.
SELECT wct.CHISQ_DIST( 0.5, --@X
1, --@Degrees_freedom
'True' --@Cumulative
) as CDF;
This produces the following result.
{"columns":[{"field":"CDF","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"}],"rows":[{"CDF":"0.520499877813047"}]}
Using the same data we calculate the chi-squared probability density function.
SELECT wct.CHISQ_DIST( 0.5, --@X
1, --@Degrees_freedom
'False' --@Cumulative
) as PDF;
This produces the following result.
{"columns":[{"field":"PDF","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"}],"rows":[{"PDF":"0.439391289467723"}]}
The chi-squared distribution is a special case of the gamma distribution.
SELECT wct.CHISQ_DIST(x, df, 'True') as [Chi-squared],
wct.GAMMAP(0.5 * df, 0.5 * x) as GammaP
FROM
(
VALUES
(42, 57)
) n (x, df);
This produces the following result.
{"columns":[{"field":"Chi-squared","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"},{"field":"GammaP","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"}],"rows":[{"Chi-squared":"0.0684558390451818","GammaP":"0.0684558390451818"}]}
See Also
CHISQ_INV - Inverse of the chi-squared distribution
CHISQ_DIST_RT - Upper chi-squared distribution
CHISQ_INV_RT - Calculate the inverse of the right-tailed probability of a chi-squared distribution.