Package cern.jet.random

Class Normal

  • All Implemented Interfaces:
    DoubleFunction, IntFunction, java.io.Serializable, java.lang.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:
    Serialized Form

    • Field Detail

      • 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 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 java.lang.String toString()
        Returns a String representation of the receiver.
        Overrides:
        toString in class java.lang.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.