ikr.simlib.distributions.continuous

• 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 $$(\alpha = 1 \mbox{ or } \alpha = k)$$ shape parameter $$\alpha > 0$$ scale parameter $$\beta > 0$$ The distribution can be alternatively described with the parameters mean value and coefficient of variation: $$\alpha = \frac{1}{c_T^2}$$ $$\beta = E[T] \cdot c_T^2$$ $$P(T=t) = f(t) = \frac{\beta^{-\alpha} \cdot t^{\alpha-1} \cdot exp(-\frac{t}{\beta})}{ \Gamma(\alpha)} \mbox{ for } t>0$$ whereby $$\Gamma(x)$$ is the gamma function exists only if $$\alpha$$ is an integer number and positive (see Erlang k distribution) $$E[T]= \alpha\beta$$ $$VAR[T]= \alpha\beta^2$$ $$c_T= \frac{1}{\sqrt{\alpha}}$$  [...].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  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)
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

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

public GammaDistribution(double alpha,
double beta)
• ### Method Detail

• #### createInstance

public static GammaDistribution createInstance(SimNode ownNode,
Parameters pars,
RandomNumberGenerator rng)
• #### next

public double next()
Description copied from class: ContinuousDistribution
Create random numbers
Specified by:
next in class ContinuousDistribution