ikr.simlib.distributions.continuous

Class BetaDistribution

java.lang.Object

ikr.simlib.distributions.Distribution

ikr.simlib.distributions.continuous.ContinuousDistribution

ikr.simlib.distributions.continuous.BetaDistribution

All Implemented Interfaces:

ReflectionConstructable, ReflectionConstructable3<SimNode,Parameters,RandomNumberGenerator>

public class BetaDistribution
extends ContinuousDistribution

Beta Distribution

Meaning:	Distribution of a random variable \(T= \frac{Z_1}{Z_1+Z_2}\), if \(Z_1\) and \(Z_2\) are gamma distributed with the parameters \(\alpha_1\) and \(\beta\) as well as \(\alpha_2\) and \(\beta\). suitable for the distribution of random shares (values between 0 and 1) Special cases contained are the uniform distribution between 0 and 1 as well as several triangular distributions
Parameters:	shape parameter \(\alpha_1 > 0\) shape parameter \(\alpha_2 > 0\) The distribution can also be described with parameters for the mean value (in the range between 0 and 1) and coefficient of variation: \(\alpha_1 = \frac{1-E[T] \cdot (1+c_T^2)}{c_T^2}\) \(\alpha_2 = \alpha_1 \cdot (\frac{1}{E[T]} -1)\)
PDF:	\(P(T=t) = f(t) = \frac{t^{\alpha_1 -1} \cdot (1-t)^{\alpha_2 -1}}{B(\alpha_1 , \alpha_2)} \mbox{ for } 0 < x < 1 \), whereby \(B(x,y)\) is the Beta function
DF:	No closed form of the distribution function (except for special cases)
Expected value:	\(E[T]= \frac{\alpha_1}{\alpha_1 + \alpha_2}\)
Variance:	\(VAR[T]= \frac{\alpha_1 \cdot \alpha_2}{(\alpha_1 + \alpha_2)^2 \cdot (\alpha_1 + \alpha_2 +1)}\)
Coefficient of variation:	\(c_T= \sqrt{\frac{\alpha_1}{\alpha_2 \cdot (\alpha_1 + \alpha_2 +1)}}\)
Parser example:	[...].Distribution = Beta [...].Distribution.Alpha1 = 1.5 [...].Distribution.Alpha2 = 3.0 or with the mean value and variation coefficient: [...].Distribution.Mean = 0.33 [...].Distribution.CoefficientOfVariation = 0.60

Field Summary

Fields

Modifier and Type	Field and Description
GammaDistribution	gamma1
GammaDistribution	gamma2

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
BetaDistribution(double alpha1, double alpha2)
BetaDistribution(double alpha1, double alpha2, RandomNumberGenerator rng)

Method Summary

Methods

Modifier and Type	Method and Description
static BetaDistribution	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

gamma1

public final GammaDistribution gamma1

gamma2

public final GammaDistribution gamma2

Constructor Detail

BetaDistribution

public BetaDistribution(double alpha1,
                double alpha2,
                RandomNumberGenerator rng)

BetaDistribution

public BetaDistribution(double alpha1,
                double alpha2)

Method Detail

createInstance

public static BetaDistribution 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