Cdf.InverseExponential Method

Evaluates the inverse of the exponential cumulative probability distribution function.

public static double InverseExponential(
double p,
double scale
);

Parameters

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

Return Value

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 InverseExponential evaluates the inverse distribution function of a gamma random variable with scale parameter =b and shape parameter a=1.0, that is, it determines $x ={\rm inverseExponential} (p, 1.0))$ , 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 documentation for routine Gamma for further discussion of the gamma distribution.

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

Cdf.InverseExponential Method

Parameters

Return Value

Remarks

See Also