I'm aware of Knuth's algorithm for generating random Poisson distributed numbers (below in Java) but how do I translate that into calling a method, generateEvent()
, randomly over time?
int poissonRandomNumber(int lambda) {
double L = Math.exp(-lambda);
int k = 0;
double p = 1;
do {
k = k + 1;
double u = Math.random();
p = p * u;
} while (p > L);
return k - 1;
}
r = poissrnd( lambda ) generates random numbers from the Poisson distribution specified by the rate parameter lambda . lambda can be a scalar, vector, matrix, or multidimensional array.
Simply choose a random point on the y-axis between 0 and 1, distributed uniformly, and locate the corresponding time value on the x-axis. For example, if we choose the point 0.2 from the top of the graph, the time until our next earthquake would be 64.38 minutes.
Revised on August 26, 2022. A Poisson distribution is a discrete probability distribution. It gives the probability of an event happening a certain number of times (k) within a given interval of time or space. The Poisson distribution has only one parameter, λ (lambda), which is the mean number of events.
The Poisson distribution is a discrete function, meaning that the variable can only take specific values in a (potentially infinite) list. Put differently, the variable cannot take all values in any continuous range.
If you are looking to simulate the inter-event arrival time, you want the exponential distribution.
Take a look at Pseudorandom Number Generator - Exponential Distribution
Your code would then look like this:
// Note L == 1 / lambda
public double poissonRandomInterarrivalDelay(double L) {
return (Math.log(1.0-Math.random())/-L;
}
...
while (true){
// Note -- lambda is 5 seconds, convert to milleseconds
long interval= (long)poissonRandomInterarrivalDelay(5.0*1000.0);
try {
Thread.sleep(interval);
fireEvent();
}
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