Random.NextExponentialMix Method

Generate a pseudorandom number from a mixture of two exponential distributions.

public virtual double NextExponentialMix(
   double theta1,
   double theta2,
   double p
);

Parameters

theta1: A double which specifies the mean of the exponential distribution that has the larger mean.
theta2: A double which specifies the mean of the exponential distribution that has the smaller mean. theta2 must be positive and less than or equal to theta1.
p: A double which specifies the mixing parameter. It must satisfy $0 \le p \le {\rm {theta1/(theta1-theta2)}}$ .

Return Value

A double which specifies a pseudorandom number from a mixture of the two exponential distributions.

Remarks

The probability density function is

$f\left( x \right) = \frac{p}{\theta }e^{ - x/\theta _1 } + \frac{{1 - p}}{{\theta _2 }}e^{ - x/\theta _2 } \,\,\, for\,x \gt 0$

where $p = \rm p$ , $\theta_1 = theta1$ , and $\theta_2 = theta2$ .

In the case of a convex mixture, that is, the case $0 \lt p \lt 1$ , the mixing parameter p is interpretable as a probability; and NextExponentialMix with probability p generates an exponential deviate with mean $\theta_1$ , and with probability 1 - p generates an exponential with mean $\theta_2$ . When p is greater than 1, but less than $\theta_1/(\theta_1 - \theta_2)$ , then either an exponential deviate with mean $\theta_2$ or the sum of two exponentials with means $\theta_1$ and $\theta_2$ is generated. The probabilities are $q = p - (p -1) \theta_1 /\theta_2$ and 1 - q, respectively, for the single exponential and the sum of the two exponentials.

Random.NextExponentialMix Method

Parameters

Return Value

Remarks

See Also