Updated: 31 July 2015

Use CHISQ_INV to calculate the inverse of the left-tailed probability of a chi-squared distribution.

SELECT [wct].[CHISQ_INV](

<@Probability, float,>

,<@Degrees_freedom, float,>)

The value of interest to be evaluated. *@Probability* must be of a type **float** or of type that intrinsically converts to **float**.

The number of degrees freedom. *@Degrees_freedom* must be of a type **float** or of a type that intrinsically converts to **float**.

float

· 0 = *@Probability* < 1

· 0 < *@Degrees_freedom*

· If *@Probability* = 0 then 0 is returned

In this example we calculate inverse of the chi-squared distribution with probability 0.975 and 10 degrees of freedom.

SELECT

wct.CHISQ_INV(

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(p,df) as [X]

,wct.INVGAMMAP(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(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.