CHIINV

Updated 2024-03-07 21:15:06.183000

Syntax

SELECT [westclintech].[wct].[CHIINV] (
  <@Probability, float,>
 ,<@Degrees_freedom, float,>)

Description

Use the scalar function CHIINV to calculate the inverse of the one-tailed probability of the chi-square distribution. The chi-square distribution is associated with a chi-square result. The chi-square distribution is a special case of the gamma distribution. Its cumulative distribution function is:

\text{F}\left(x;k\right)=\frac{\gamma(k\slash2,x\slash2)}{\Gamma(k\slash2)}

Where γ(s,t) is the lower incomplete gamma function.

Arguments

@Probability

is any number between zero and one. @Probability is an expression of type float or of a type that can be implicitly converted to float.

@Degrees_freedom

is any real positive number. @Degrees_freedom is an expression of type float or of a type that can be implicitly converted to float.

Return Type

float

Remarks

If @Probability < 0 or @Probability> 1, CHIINV returns an error.

@Degrees_freedom is truncated to zero decimal places.

if @Degrees_freedom < 1 or @Degrees_freedom > 10^10, CHIINV returns an error.

CHIINV uses root-finding algorithms and iteration to solve for CHIDIST(CHIINV(@Probability, @Degrees_freedom),@Degrees_freedom)-@Probability = 0 to eight decimal places.

CHIINV = GAMMAINV(1-@Probability, @Degrees_freedom/2, 2)

Examples

select wct.CHIINV(.01, 5);

This produces the following result.

{"columns":[{"field":"column 1","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"}],"rows":[{"column 1":"15.0862724691398"}]}

select round(wct.CHIDIST(wct.CHIINV(.01, 5), 5) - .01, 8);

This produces the following result.

{"columns":[{"field":"column 1","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"}],"rows":[{"column 1":"0"}]}

Select wct.GAMMAINV(1 - .01, 2.5, 2);

This produces the following result.

----------------------
       15.086272469389