Computes the normalized lower (left) incomplete Gamma function.

Namespace: Meta.Numerics.Functions
Assembly: Meta.Numerics (in Meta.Numerics.dll) Version: 2.1.0.0 (2.1.0.0)

Syntax

            
 C#  Visual Basic  Visual C++  F# 
public static double LeftRegularizedGamma(
	double a,
	double x
)
Public Shared Function LeftRegularizedGamma ( _
	a As Double, _
	x As Double _
) As Double
public:
static double LeftRegularizedGamma(
	double a, 
	double x
)
static member LeftRegularizedGamma : 
        a : float * 
        x : float -> float 

Parameters

a
Double
The shape parameter, which must be positive.
x
Double
The argument, which must be non-negative.

Return Value

The value of γ(a,x)/Γ(x).

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.

Exceptions

ExceptionCondition
System..::..ArgumentOutOfRangeExceptiona is negative or zero.
System..::..ArgumentOutOfRangeExceptionx is negative.

See Also