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

Namespace: Imsl.Stat
Assembly: ImslCS (in ImslCS.dll) Version: 6.5.2.0
Syntax
Copy
public virtual double NextExponentialMix(
	double theta1,
	double theta2,
	double p
)

Parameters

theta1
Type: SystemDouble
A double which specifies the mean of the exponential distribution that has the larger mean.
theta2
Type: SystemDouble
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
Type: SystemDouble
A double which specifies the mixing parameter. It must satisfy 0 \le p \le {\rm {theta1/(theta1-theta2)}}.

Return Value

Type: Double
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.

See Also