SQL Server CHISQ_INV Function

Updated 2023-11-02 21:11:42.813000

Description

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

Syntax

SELECT [westclintech].[wct].[CHISQ_INV](
  <@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 = 0 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(   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.

See Also

CHISQ_DIST - Lower chi-squared distribution

CHISQ_INV_RT - Calculate the inverse of the right-tailed probability of a chi-squared distribution.

CHISQ_DIST_RT - Upper chi-squared distribution

INVGAMMAP - Calculate the inverse of the incomplete gamma functionP(a,x).