INVGAMMAP

Updated 2024-03-08 16:38:52.673000

Syntax

SELECT [westclintech].[wct].[INVGAMMAP] (
   <@P, float,>
 ,<@A, float,>)

Use the scalar function INVGAMMAP to calculate the inverse of the incomplete gamma function P(a,x). The equation for this function is:

P(a,x)=\frac{\gamma(a,x)}{\Gamma(a)}

Where γ(a, x) is an incomplete gamma function and Γ(a) is the gamma function and where

\gamma(a,x)+\Gamma(a)=1

a value to be passed to the function. @A is an expression of type float or of a type that can be implicitly converted to float.

a value to be passed to the function. @P is an expression of type float or of a type that can be implicitly converted to float.

float

If @A = 0, INVGAMMAP will return an error.

GAMMAP(@A,INVGAMMAP(@P, @A))-@P = 0

Select wct.INVGAMMAP(0.0526530172876507, 5);

This produces the following result.

{"columns":[{"field":"column 1","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"}],"rows":[{"column 1":"2"}]}

Select wct.GAMMAP(5, wct.INVGAMMAP(0.0526530172876507, 5)) - 0.0526530172876507;

This produces the following result.

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