randomExponentialMix¶

Generates pseudorandom numbers from a mixture of two exponential distributions.

Synopsis¶

randomExponentialMix (nRandom, theta1, theta2, p)

Required Arguments¶

int nRandom (Input): Number of random numbers to generate.
float theta1 (Input): Mean of the exponential distribution which has the larger mean.
float theta2 (Input): Mean of the exponential distribution which has the smaller mean. Parameter theta2 must be positive and less than or equal to theta1.
float p (Input): Mixing parameter. Parameter p must be non-negative and less than or equal to theta1/(theta1 − theta2).

Return Value¶

An array of length nRandom containing the random deviates of a mixture of two exponential distributions.

Description¶

Function randomExponentialMix generates pseudorandom numbers from a mixture of two exponential distributions. The probability density function is

$f(x) = \frac{p}{\theta_1} e^{-x/\theta_1} + \frac{1-p}{\theta_2} e^{-x/\theta_2}$

for $x>0$ , where p = p, $\theta_1$ = theta1, and $\theta_2$ = theta2.

In the case of a convex mixture, that is, the case $0<p<1$ , the mixing parameter p is interpretable as a probability; and randomExponentialMix 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 $\theta_1$ 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.

Example¶

In this example, randomExponentialMix is used to generate five pseudorandom deviates from a mixture of exponentials with means 2 and 1, respectively, and with mixing parameter 0.5.

from numpy import *
from pyimsl.stat.randomExponentialMix import randomExponentialMix
from pyimsl.stat.randomSeedSet import randomSeedSet
from pyimsl.stat.writeMatrix import writeMatrix

n_random = 5
theta1 = 2.0
theta2 = 1.0
p = 0.5
randomSeedSet(123457)
r = randomExponentialMix(n_random, theta1, theta2, p)
writeMatrix("Mixed exponential random deviates: ", r,
            noColLabels=True)

Output¶

 
              Mixed exponential random deviates: 
      0.070        1.302        0.630        1.976        0.372