ikr.simlib.distributions.continuous

Class WeibullDistribution

java.lang.Object

ikr.simlib.distributions.Distribution

ikr.simlib.distributions.continuous.ContinuousDistribution

ikr.simlib.distributions.continuous.WeibullDistribution

All Implemented Interfaces:

ReflectionConstructable, ReflectionConstructable3<SimNode,Parameters,RandomNumberGenerator>

public class WeibullDistribution
extends ContinuousDistribution

Weibull Distribution

Meaning:	The Weibull distribution is often used to model internet traffic because of its heavy tail.
Parameters:	shape parameter $\alpha > 0$ scale parameter $\beta > 0$
PDF:	$P(T=t) = f(t) = \alpha \cdot \beta^{-\alpha} \cdot t^{\alpha -1} \cdot exp(-(\frac{t}{\beta})^{\alpha}) \mbox{ for } t>0$
DF:	$P(T \le t) = F(t) = 1- exp(-(\frac{t}{\beta})^{\alpha}) \mbox{ for } t>0$
Expected value:	$E[T]= \frac{\beta}{\alpha} \cdot \Gamma(\frac{1}{\alpha}$, whereas $\Gamma(x)$ is the gamma function
Variance:	$VAR[T]= \frac{\beta^2}{\alpha} \cdot \left\{ 2\Gamma(\frac{2}{\alpha}) - \frac{1}{\alpha} \cdot \Gamma(\frac{1}{\alpha})^2 \right\}$
Coefficient of variation:	$c_T= \sqrt{\frac{2\alpha\Gamma(\frac{2}{\alpha})}{(\Gamma(\frac{1}{\alpha}))^2} -1}$
Parser example:	[...].Distribution = Weibull [...].Distribution.Alpha = 0.3 [...].Distribution.Beta = 0.03

Field Summary

Fields

Modifier and Type	Field and Description
double	alphaReciprocal
double	beta

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

Method Summary

Methods

Modifier and Type	Method and Description
static WeibullDistribution	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

alphaReciprocal

public final double alphaReciprocal

beta

public final double beta

Constructor Detail

WeibullDistribution

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

WeibullDistribution

public WeibullDistribution(double alpha,
                   double beta)

Method Detail

createInstance

public static WeibullDistribution 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