ikr.simlib.distributions.continuous

Class NormalDistribution

java.lang.Object

ikr.simlib.distributions.Distribution

ikr.simlib.distributions.continuous.ContinuousDistribution

ikr.simlib.distributions.continuous.NormalDistribution

All Implemented Interfaces:

ReflectionConstructable, ReflectionConstructable3<SimNode,Parameters,RandomNumberGenerator>

public class NormalDistribution
extends ContinuousDistribution

Normal Distribution

Meaning:	Limit distribution of the sum of many independent random variables with arbitrary statistical characteristics, if the contribution of a single random variable remains neglectably small.
Parameters:	mean value \(\mu\) standart deviation \(\sigma > 0\)
PDF:	\(P(T=t) = f(t) = \frac{1}{\sqrt{2 \pi} \sigma} \cdot exp( -\frac{(t- \mu)^2}{2\sigma^2} )\)
DF:	\(P(T \le t) = F(t) = \frac{1}{2} \cdot erf(\frac{t-\mu}{\sqrt{2} \sigma}) \mbox{ with } erf(x) = \frac{2}{\sqrt{\pi}} \cdot \int_0^x \! exp(-y^2) \, dy \)
Expected value:	\(E[T]= \mu \)
Variance:	\(VAR[T]= \sigma^2\)
Coefficient of variation:	\(c_T= \frac{\sigma}{\mu}\)
LST:	\(\phi(s) = exp(-\mu s + \frac{(s \sigma)^2}{2})\)
Parser example:	[...].Distribution = Normal [...].Distribution.Mean = 6.3 [...].Distribution.StandardDeviation = 1.5

Field Summary

Fields

Modifier and Type	Field and Description
double	mean
double	standardDeviation

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
NormalDistribution(double mean, double standardDeviation)
NormalDistribution(double mean, double standardDeviation, RandomNumberGenerator rng)

Method Summary

Methods

Modifier and Type	Method and Description
static NormalDistribution	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

mean

public final double mean

standardDeviation

public final double standardDeviation

Constructor Detail

NormalDistribution

public NormalDistribution(double mean,
                  double standardDeviation,
                  RandomNumberGenerator rng)

NormalDistribution

public NormalDistribution(double mean,
                  double standardDeviation)

Method Detail

createInstance

public static NormalDistribution 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