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## 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:
  Cloneable, DoubleFunction, IntFunction, Serializable

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
See Also:
  Serialized Form

Field Summary

Fields inherited from class cern.colt.PersistentObject
`serialVersionUID`

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

Method Summary
`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.

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