cern.jet.random

Class Normal

java.lang.Object

cern.colt.PersistentObject

cern.jet.random.AbstractDistribution

cern.jet.random.AbstractContinousDistribution

cern.jet.random.Normal

All Implemented Interfaces:

DoubleFunction, IntFunction, Serializable, Cloneable

public class Normal
extends AbstractContinousDistribution

Normal (aka Gaussian) distribution; See the math definition and animated definition.

                       
                                   1                       2
          pdf(x) = ---------    exp( - (x-mean) / 2v ) 
                           sqrt(2pi*v)

                                                        x
                                                         -
                                   1        | |                 2
          cdf(x) = ---------    |    exp( - (t-mean) / 2v ) dt
                           sqrt(2pi*v)| |
                                                   -
                                                  -inf.

where v = variance = standardDeviation^2.

Instance methods operate on a user supplied uniform random number generator; they are unsynchronized.

Static methods operate on a default uniform random number generator; they are synchronized.

Implementation: Polar Box-Muller transformation. See G.E.P. Box, M.E. Muller (1958): A note on the generation of random normal deviates, Annals Math. Statist. 29, 610-611.

Version:

1.0, 09/24/99

Author:

wolfgang.hoschek@cern.ch

See Also:

Serialized Form

Field Summary

Fields

Modifier and Type	Field and Description
protected double	cache
protected boolean	cacheFilled
protected double	mean
protected static Normal	shared
protected double	SQRT_INV
protected double	standardDeviation
protected double	variance

Fields inherited from class cern.jet.random.AbstractDistribution

randomGenerator

Fields inherited from class cern.colt.PersistentObject

serialVersionUID

Constructor Summary

Constructors

Constructor and Description
Normal(double mean, double standardDeviation, RandomEngine randomGenerator) Constructs a normal (gauss) distribution.

Method Summary

Methods

Modifier and Type	Method and Description
double	cdf(double x) Returns the cumulative distribution function.
double	nextDouble() Returns a random number from the distribution.
double	nextDouble(double mean, double standardDeviation) Returns a random number from the distribution; bypasses the internal state.
double	pdf(double x) Returns the probability distribution function.
protected void	setRandomGenerator(RandomEngine randomGenerator) Sets the uniform random generator internally used.
void	setState(double mean, double standardDeviation) Sets the mean and variance.
static double	staticNextDouble(double mean, double standardDeviation) Returns a random number from the distribution with the given mean and standard deviation.
String	toString() Returns a String representation of the receiver.

Methods inherited from class cern.jet.random.AbstractDistribution

apply, apply, clone, getRandomGenerator, makeDefaultGenerator, nextInt

Methods inherited from class java.lang.Object

equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

Field Detail

mean

protected double mean

variance

protected double variance

standardDeviation

protected double standardDeviation

cache

protected double cache

cacheFilled

protected boolean cacheFilled

SQRT_INV

protected double SQRT_INV

shared

protected static Normal shared

Constructor Detail

Normal

public Normal(double mean,
      double standardDeviation,
      RandomEngine randomGenerator)

Constructs a normal (gauss) distribution. Example: mean=0.0, standardDeviation=1.0.

Method Detail

cdf

public double cdf(double x)

Returns the cumulative distribution function.

nextDouble

public double nextDouble()

Returns a random number from the distribution.

Specified by:

nextDouble in class AbstractDistribution

nextDouble

public double nextDouble(double mean,
                double standardDeviation)

Returns a random number from the distribution; bypasses the internal state.

pdf

public double pdf(double x)

Returns the probability distribution function.

setRandomGenerator

protected void setRandomGenerator(RandomEngine randomGenerator)

Sets the uniform random generator internally used.

Overrides:

setRandomGenerator in class AbstractDistribution

setState

public void setState(double mean,
            double standardDeviation)

Sets the mean and variance.

staticNextDouble

public static double staticNextDouble(double mean,
                      double standardDeviation)

Returns a random number from the distribution with the given mean and standard deviation.

toString

public String toString()

Returns a String representation of the receiver.

Overrides:

toString in class Object