 # SQL Server CHISQ.INV.RT function

CHISQ_INV_RT

Updated: 31 July 2015

Use CHISQ_INV_RT to calculate the inverse of the right-tailed probability of a chi-squared distribution.
Syntax
SELECT [wct].[CHISQ_INV_RT](
<@Probability, float,>
,<@Degrees_freedom, float,>)
Arguments
@Probability
The value of interest to be evaluated. @Probability 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 < @Probability = 1
·         0 < @Degrees_freedom
·         If @Probability = 1 then 0 is returned
Examples
In this example we calculate inverse of the chi-squared distribution with probability 0.975 and 10 degrees of freedom.
SELECT
wct.CHISQ_INV_RT(
0.95         --@Probability
,10           --@Degrees_freedom
) as [X]

This produces the following result

The chi-squared distribution is a special case of the gamma distribution
SELECT
wct.CHISQ_INV_RT(p,df) as [X]
,wct.INVGAMMAP(1-p,0.5*df)*2 as [X]
FROM (VALUES (0.95,10))n(p,df)

This produces the following result.

This example returns a table of critical values for the distribution.
SELECT
df,[0.99],[0.95],[0.90],[0.75],[0.50],[0.25],[0.10],[0.05],[0.01]
FROM (
SELECT
df
,p
,wct.CHISQ_INV_RT(p,df) as x
FROM
(VALUES (0.99),(0.95),(0.90),(0.75),(0.50),(0.25),(0.10),(0.05),(0.01))n(p)
CROSS APPLY
(VALUES (1),(2),(3),(4),(5),(6),(7),(8),(9),(10),(11),(12),(13),(14),(15),(16),(17),(18),(19),(20),(22),(24),(26),(28),(30),(40),(50),(60))m(df)
)p
PIVOT(
max(x)
FOR p IN([0.99],[0.95],[0.90],[0.75],[0.50],[0.25],[0.10],[0.05],[0.01])
) d

This produces the following result.

### Support  Copyright 2008-2022 Westclintech LLC         Privacy Policy        Terms of Service