InvCdf.Exponential Method

InvCdfExponential Method

Evaluates the inverse of the exponential cumulative probability distribution function.

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

Syntax

public static double Exponential(
	double p,
	double scale
)

Public Shared Function Exponential ( 
	p As Double,
	scale As Double
) As Double

public:
static double Exponential(
	double p, 
	double scale
)

static member Exponential : 
        p : float * 
        scale : float -> float

Parameters

p: Type: SystemDouble
A double scalar value representing the probability at which the function is to be evaluated.
scale: Type: SystemDouble
A double scalar value representing the scale parameter.

Return Value

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

Remarks

Method InvCdf.Exponential evaluates the inverse distribution function of a Gamma random variable with scale parameter =b and shape parameter a=1.0, that is, it determines $x={\rm{exponential}}(p,1.0))$ , such that

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

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.Exponential 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