ikr.simlib.distributions.continuous

## Class ErlangDistribution

• All Implemented Interfaces:
ReflectionConstructable, ReflectionConstructable3<SimNode,Parameters,RandomNumberGenerator>

public class ErlangDistribution
extends ContinuousDistribution
Erlang k Distribution

Erlang k distribution
Meaning: Distribution for the sum of $$k$$ random variables that are each negative-exponentially distributed with the parameter $$\lambda$$ (serial switch in the phase model). order $$k>0$$ rate $$\lambda > 0$$ of the individual phases or total mean value $$m = \frac{k}{\lambda}$$ $$P(T=t) = f(t) = \lambda \cdot \frac{(\lambda t)^{k-1}}{(k-1)!} \cdot exp(-\lambda t)$$ $$P(T \le t) = F(t) = 1 - exp(-\lambda t) \cdot \sum\limits_{i=0}^{k-1} \frac{(\lambda t)^i}{i!}$$ $$E[T]= \frac{k}{\lambda} = m$$ $$VAR[T]= \frac{k}{\lambda^2} = \frac{m^2}{k}$$ $$c_T= \frac{1}{\sqrt{k}} \le 1$$ $$\phi(s) = (\frac{\lambda}{\lambda +s})^k = (\frac{1}{1+ms})^k$$ [...].Distribution = Erlang [...].Distribution.Mean = 4.5 # k/lambda [...].Distribution.Order = 3 # number of phases (k)