Cdf.Exponential Method

Evaluates the exponential cumulative probability distribution function.

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

Parameters

x: A double scalar value representing the argument at which the function is to be evaluated.
scale: A double scalar value representing the scale parameter, b.

Return Value

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

Remarks

Method 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, Gamma uses a series expansion. Otherwise, a continued fraction expansion is used. (See Abramowitz and Stegun, 1964.)

Plot of Exponential Distribution Function

Cdf.Exponential Method

Parameters

Return Value

Remarks

See Also