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.

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

Method Summary

All Methods Static Methods Instance Methods Concrete 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.
`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

Class Normal

Field Summary

Fields inherited from class cern.colt.PersistentObject

Constructor Summary

Method Summary

Methods inherited from class cern.jet.random.AbstractDistribution

Methods inherited from class java.lang.Object

Constructor Detail

Normal

Method Detail

cdf

nextDouble

nextDouble

pdf

setState

staticNextDouble

toString