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
See Also:

  • Field Details

    • 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 Details

    • Normal

      public Normal(double mean, double standardDeviation, RandomEngine randomGenerator)
      Constructs a normal (gauss) distribution. Example: mean=0.0, standardDeviation=1.0.

  • Method Details

    • 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

    • xstaticSetRandomGenerator

      private static void xstaticSetRandomGenerator(RandomEngine randomGenerator)
      Sets the uniform random number generated shared by all static methods.
      Parameters:
      randomGenerator - the new uniform random number generator to be shared.