ikr.simlib.distributions.continuous

Class ErlangDistribution

java.lang.Object

ikr.simlib.distributions.Distribution

ikr.simlib.distributions.continuous.ContinuousDistribution

ikr.simlib.distributions.continuous.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).
Parameters:	order \(k>0\) rate \(\lambda > 0\) of the individual phases or total mean value \(m = \frac{k}{\lambda}\)
PDF:	\(P(T=t) = f(t) = \lambda \cdot \frac{(\lambda t)^{k-1}}{(k-1)!} \cdot exp(-\lambda t)\)
DF:	\(P(T \le t) = F(t) = 1 - exp(-\lambda t) \cdot \sum\limits_{i=0}^{k-1} \frac{(\lambda t)^i}{i!} \)
Expected value:	\(E[T]= \frac{k}{\lambda} = m\)
Variance:	\(VAR[T]= \frac{k}{\lambda^2} = \frac{m^2}{k}\)
Coefficient of variation:	\(c_T= \frac{1}{\sqrt{k}} \le 1\)
LST:	\(\phi(s) = (\frac{\lambda}{\lambda +s})^k = (\frac{1}{1+ms})^k\)
Parser example:	[...].Distribution = Erlang [...].Distribution.Mean = 4.5 # k/lambda [...].Distribution.Order = 3 # number of phases (k)

Field Summary

Fields

Modifier and Type	Field and Description
int	order
NegExpDistribution	phase

Fields inherited from class ikr.simlib.distributions.Distribution

rng

Fields inherited from interface ikr.simlib.parameters.reflection.ReflectionConstructable

CREATE_INSTANCE_METHOD_NAME

Constructor Summary

Constructors

Constructor and Description
ErlangDistribution(double mean, int order)
ErlangDistribution(double mean, int order, RandomNumberGenerator rng)

Method Summary

Methods

Modifier and Type	Method and Description
static ErlangDistribution	createInstance(SimNode ownNode, Parameters pars, RandomNumberGenerator rng) as required by ReflectionConstructable
double	next() Create random numbers

Methods inherited from class ikr.simlib.distributions.Distribution

getDefaultRNG, getRandomNumberGenerator, reset

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail

order

public final int order

phase

public final NegExpDistribution phase

Constructor Detail

ErlangDistribution

public ErlangDistribution(double mean,
                  int order,
                  RandomNumberGenerator rng)

ErlangDistribution

public ErlangDistribution(double mean,
                  int order)

Method Detail

createInstance

public static ErlangDistribution createInstance(SimNode ownNode,
                                Parameters pars,
                                RandomNumberGenerator rng)

as required by ReflectionConstructable

next

public double next()

Description copied from class: ContinuousDistribution

Create random numbers

Specified by:

next in class ContinuousDistribution