In Java, I have a set of users, each of which has a Poisson-distributed demand with a known mean:
import org.apache.commons.math3.distribution.PoissonDistribution;
public class User {
private int mean;
private PoissonDistribution dist;
public void setMean(int mean) {
this.mean = mean;
this.poissonDistribution = new PoissonDistribution(mean);
}
}
...
User u1 = new User(); u1.setMean(20);
User u2 = new User(); u2.setMean(30);
User u3 = new User(); u3.setMean(40);
Now I'd like to calculate the probability that all User
s have a cumulated demand below a certain value:
double probabilityBelowX = calculateCumulatedProbability(50, u1, u2, u3); // <- what must this method look like?
I am stuck at the question, how to solve this problem in Java. Am I missing something in the math package? I know that the demands of the customers are independent, so according to my knowledge about the Poisson distribution I can simply add up the values. But I only have cumulativeProbability(int x)
for every single one of the user demands, but not for several at once.