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GAMMAQ

Updated 2024-03-08 16:05:14.760000

Syntax

SELECT [westclintech].[wct].[GAMMAQ] (
  <@A, float,>
 ,<@X, float,>)

Description

Use the scalar function GAMMAQ to calculate the regularized gamma function Q(a, x). The equation for this function is:

Q(a,x)=\frac{\Gamma(a,x)}{\Gamma(a)}

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

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

Arguments

@A

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.

@X

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

Return Type

float

Remarks

If @A < 0 or @X < 0, GAMMAQ returns an error.

GAMMAP(@A, @X) + GAMMAQ(@A, @X) = 1.

Examples

Select wct.GAMMAQ(5, 2);

This produces the following result.

{"columns":[{"field":"column 1","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"}],"rows":[{"column 1":"0.947346982712349"}]}
Select wct.GAMMAINC(5, 2) / wct.gamma(5);

This produces the following result.

{"columns":[{"field":"column 1","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"}],"rows":[{"column 1":"0.947346982712349"}]}
Select wct.GAMMAP(5, 2) + wct.GAMMAQ(5, 2);

This produces the following result.

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

See Also

GAMMAP - lower regularized gamma function

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

GAMMADIST - gamma distribution

GAMMAINV - inverse gamma function

BETADIST - beta distribution

CHIDIST - chi-square distribution

GAMMA - complete gamma function

GAMMAINC - incomplete gamma function

GAMMALN - natural logarithm of the complete gamma function