Cdf.Exponential Method

CdfExponential Method

Evaluates 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 x,
	double scale
)

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

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

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

Parameters

x: Type: SystemDouble
A double scalar value representing the argument 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 representing the probability that an exponential random variable takes on a value less than or equal to x.

Remarks

Method Cdf.Exponential is a special case of the gamma distribution function, which evaluates the distribution function, F, with scale parameter b and shape parameter a, used in the gamma distribution function equal to 1.0. That is,

$F\left(x\right)=\frac{1}{{\Gamma\left(a \right)}}\int_0^x {e^{-t/b}}dt$

where $\Gamma(\cdot)$ is the gamma function. (The gamma function is the integral from 0 to $\infty$ of the same integrand as above). The value of the distribution function at the point x is the probability that the random variable takes a value less than or equal to x.

If x is less than or equal to 1.0, Cdf.Gamma uses a series expansion. Otherwise, a continued fraction expansion is used. (See Abramowitz and Stegun, 1964.)

Plot of Exponential Distribution Function

Reference

Cdf Class

Imsl.Stat Namespace

Other Resources

Example