Updated: 9 August 2010

Use FINV to calculate the inverse of the F probability distribution. A frequent use of the F-distribution is to test whether two observed samples have the same variance. The F-distribution cumulative distribution function (cdf) is given in terms of the incomplete beta function:

SELECT [wctStatistics].[wct].[FINV] (

<@Probability, float,>

,<@Degrees_freedom1, float,>

,<@Degrees_freedom2, float,>)

is a probability associated with the F-distribution cdf. *@Probability *is an expression of type **float** or of a type that can be implicitly converted to **float**.

is the numerator degrees of freedom. *@Degrees_freedom1 *is an expression of type **float** or of a type that can be implicitly converted to **float**.

is the denominator degrees of freedom. *@Degrees_freedom2 *is an expression of type **float** or of a type that can be implicitly converted to **float**.

float

· If *@Probability *< 0 or *@Probability* > 1, FINV returns an error.

· *@Degrees_freedom1 *and* @Degrees_freedom2 * are truncated to zero decimal places.

· If *@Degrees_freedom1* < 1 or *@Degrees_freedom1 *> 10^10, FINV returns an error.

· If *@Degrees_freedom2* < 1 or *@Degrees_freedom2 *> 10^10, FINV returns an error.

· FINV uses root-finding algorithms and iteration to satisfy the condition that

FDIST(FINV(*@Probability,@Degrees_freedom1, @Degrees_freedom2*),* @Degrees_freedom1*, *@Degrees_freedom2*)-*@Probability* = 0 to eight decimal places.

Select wct.FINV(.05, 6, 10)

This produces the following result

----------------------

3.21717454739921

(1 row(s) affected)

Select round(wct.FDIST(wct.FINV(.05, 6, 10), 6, 10)-.05, 8)

This produces the following result

----------------------

0

(1 row(s) affected)