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.

See Also:

Serialized Form

Field Summary

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

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.
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, makeDefaultGenerator, nextInt

Methods inherited from class java.lang.Object

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

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.

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