Normal
cern.jet.random

Class Normal

  • All Implemented Interfaces:
    DoubleFunction, IntFunction, Serializable, Cloneable


    public class Normalextends AbstractContinousDistribution
    Normal (aka Gaussian) distribution; See the math definitionand 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
    • Constructor Summary

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

      Methods 
      Modifier and TypeMethod and Description
      doublecdf(double x)
      Returns the cumulative distribution function.
      doublenextDouble()
      Returns a random number from the distribution.
      doublenextDouble(double mean, double standardDeviation)
      Returns a random number from the distribution; bypasses the internal state.
      doublepdf(double x)
      Returns the probability distribution function.
      voidsetState(double mean, double standardDeviation)
      Sets the mean and variance.
      static doublestaticNextDouble(double mean, double standardDeviation)
      Returns a random number from the distribution with the given mean and standard deviation.
      StringtoString()
      Returns a String representation of the receiver.
    • 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(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

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