public class PoissonDistribution extends DiscreteDistribution
| Meaning: | Probability of the number of arrivals in a time interval with the duration \(t\) for a Markovian arrival process (limit distribution of a binomial distribution for \(n \to \infty , q \to 0, nq \to \lambda t\)) |
|---|---|
| Parameters: | mean value \(m = \lambda t > 0\) |
| Distribution: | \(P(X=i) = \frac{(\lambda t)^i}{i!} \cdot exp(-\lambda t) = \frac{m^i}{i!} \cdot exp(-m) \) |
| Expected value: | \(E[X]= \lambda t = m \) |
| Variance: | \(VAR[X]= \lambda t = m\) |
| Coefficient of variation: | \(c_T=\frac{1}{ \sqrt{ \lambda t }} = \frac{1}{ \sqrt{m}}\) |
| Generating func.: | \(G(z)= exp(-\lambda t \cdot (1-z)) = exp(-m \cdot (1-z))\) |
| Parser example: |
[...].Distribution = Poisson
|
| Modifier and Type | Field and Description |
|---|---|
double |
expNegMean |
rngCREATE_INSTANCE_METHOD_NAME| Constructor and Description |
|---|
PoissonDistribution(double mean) |
PoissonDistribution(double mean,
RandomNumberGenerator rng) |
| Modifier and Type | Method and Description |
|---|---|
static PoissonDistribution |
createInstance(SimNode ownNode,
Parameters pars,
RandomNumberGenerator rng)
as required by
ReflectionConstructable |
int |
next()
Create random numbers
|
getDefaultRNG, getRandomNumberGenerator, resetpublic PoissonDistribution(double mean,
RandomNumberGenerator rng)
public PoissonDistribution(double mean)
public static PoissonDistribution createInstance(SimNode ownNode, Parameters pars, RandomNumberGenerator rng)
ReflectionConstructablepublic int next()
DiscreteDistributionnext in class DiscreteDistribution