AdvancedMath.LeftRegularizedGamma Method
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AdvancedMathLeftRegularizedGamma Method

Computes the normalized lower (left) incomplete Gamma function.

Namespace:  Meta.Numerics.Functions
Assembly:  Meta.Numerics (in Meta.Numerics.dll) Version: 4.0.5.0 (4.0.5.0)
Syntax
public static double LeftRegularizedGamma(
	double a,
	double x
)

Parameters

a
Type: SystemDouble
The shape parameter, which must be positive.
x
Type: SystemDouble
The argument, which must be non-negative.

Return Value

Type: Double
The value of γ(a,x)/Γ(a).
Exceptions
ExceptionCondition
ArgumentOutOfRangeExceptiona is negative or zero, or x is negative.
Remarks

The incomplete Gamma function is obtained by carrying out the Gamma function integration from zero to some finite value x, instead of to infinity. The function is normalized by dividing by the complete integral, so the function ranges from 0 to 1 as x ranges from 0 to infinity.

For large values of x, this function becomes 1 within floating point precision. To determine its deviation from 1 in this region, use the complementary function RightRegularizedGamma(Double, Double).

For a=ν/2 and x=χ2/2, this function is the CDF of the χ2 distribution with ν degrees of freedom.

See Also