InvCdf.Gamma Method

InvCdfGamma Method

Evaluates the inverse of the Gamma cumulative probability distribution function.

Namespace: Imsl.Stat
Assembly: ImslCS (in ImslCS.dll) Version: 6.5.2.0

Syntax

public static double Gamma(
	double p,
	double a
)

Public Shared Function Gamma ( 
	p As Double,
	a As Double
) As Double

public:
static double Gamma(
	double p, 
	double a
)

static member Gamma : 
        p : float * 
        a : float -> float

Parameters

p: Type: SystemDouble
A double scalar value representing the probability at which the function is to be evaluated.
a: Type: SystemDouble
A double scalar value representing the shape parameter. This must be positive.

Return Value

Type: Double
A double scalar value. The probability that a Gamma random variable takes a value less than or equal to this returned value is p.

Remarks

Method InvCdf.Gamma evaluates the inverse distribution function of a Gamma random variable with shape parameter a, that is, it determines $x={\rm{Gamma}}(p,a))$ , such that

$P=\frac{1}{{\Gamma\left(a\right)}} \int_o^x{e^{-t}}t^{a-1}dt$

where $\Gamma(\cdot)$ is the Gamma function. The probability that the random variable takes a value less than or equal to x is P. See the Cdf.Gamma remarks for further discussion of the Gamma distribution.

InvCdf.Gamma uses bisection and modified regula falsi to invert the distribution function, which is evaluated using method Cdf.Gamma.

Reference

InvCdf Class

Imsl.Stat Namespace

Other Resources

Example