ikr.simlib.distributions.continuous

Class GammaDistribution

java.lang.Object

ikr.simlib.distributions.Distribution

ikr.simlib.distributions.continuous.ContinuousDistribution

ikr.simlib.distributions.continuous.GammaDistribution

All Implemented Interfaces:

ReflectionConstructable, ReflectionConstructable3<SimNode,Parameters,RandomNumberGenerator>

public class GammaDistribution
extends ContinuousDistribution

Gamma Distribution

Meaning:	The gamma distribution may, e.g., be applied to characterize video traffic. Special cases contained are the negative-exponential and Erlang k distribution \((\alpha = 1 \mbox{ or } \alpha = k)\)
Parameters:	shape parameter \(\alpha > 0\) scale parameter \(\beta > 0\) The distribution can be alternatively described with the parameters mean value and coefficient of variation: \(\alpha = \frac{1}{c_T^2}\) \(\beta = E[T] \cdot c_T^2\)
PDF:	\(P(T=t) = f(t) = \frac{\beta^{-\alpha} \cdot t^{\alpha-1} \cdot exp(-\frac{t}{\beta})}{ \Gamma(\alpha)} \mbox{ for } t>0\) whereby \(\Gamma(x)\) is the gamma function
DF:	exists only if \(\alpha\) is an integer number and positive (see Erlang k distribution)
Expected value:	\(E[T]= \alpha\beta\)
Variance:	\(VAR[T]= \alpha\beta^2\)
Coefficient of variation:	\(c_T= \frac{1}{\sqrt{\alpha}}\)
Parser example:	[...].Distribution = Gamma [...].Distribution.Alpha = 0.44 [...].Distribution.Beta = 10.13 or with the mean value and variation coefficient: [...].Distribution.Mean = 4.5 [...].Distribution.CoefficientOfVariation = 1.5
References:	Law/Kelton fourth edition, pp. 284-286

Field Summary

Fields

Modifier and Type	Field and Description
double	A
double	alpha
double	B
double	beta
double	D
double	Q
double	theta

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
GammaDistribution(double alpha, double beta)
GammaDistribution(double alpha, double beta, RandomNumberGenerator rng)

Method Summary

Methods

Modifier and Type	Method and Description
static GammaDistribution	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

alpha

public final double alpha

beta

public final double beta

A

public final double A

B

public final double B

D

public final double D

Q

public final double Q

theta

public final double theta

Constructor Detail

GammaDistribution

public GammaDistribution(double alpha,
                 double beta,
                 RandomNumberGenerator rng)

GammaDistribution

public GammaDistribution(double alpha,
                 double beta)

Method Detail

createInstance

public static GammaDistribution 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