Package org.apache.commons.statistics.distribution

Class NormalDistribution

java.lang.Object
org.apache.commons.statistics.distribution.NormalDistribution
All Implemented Interfaces:
ContinuousDistribution
public class NormalDistribution
extends java.lang.Object
Implementation of the normal (Gaussian) distribution.

  • Nested Class Summary

    Nested classes/interfaces inherited from interface org.apache.commons.statistics.distribution.ContinuousDistribution

    ContinuousDistribution.Sampler

  • Constructor Summary

    Constructors 
    Constructor Description
    NormalDistribution​(double mean, double sd)
    Creates a distribution.

  • Method Summary

    Modifier and Type Method Description
    ContinuousDistribution.Sampler createSampler​(UniformRandomProvider rng)
    Creates a sampler.
    double cumulativeProbability​(double x)
    For a random variable X whose values are distributed according to this distribution, this method returns P(X <= x).
    double density​(double x)
    Returns the probability density function (PDF) of this distribution evaluated at the specified point x.
    double getMean()
    Gets the mean of this distribution.
    double getStandardDeviation()
    Access the standard deviation.
    double getSupportLowerBound()
    Gets the lower bound of the support.
    double getSupportUpperBound()
    Gets the upper bound of the support.
    double getVariance()
    Gets the variance of this distribution.
    double inverseCumulativeProbability​(double p)
    Computes the quantile function of this distribution.
    boolean isSupportConnected()
    Indicates whether the support is connected, i.e.
    double logDensity​(double x)
    Returns the natural logarithm of the probability density function (PDF) of this distribution evaluated at the specified point x.
    double probability​(double x0, double x1)
    For a random variable X whose values are distributed according to this distribution, this method returns P(x0 < X <= x1).
    static double[] sample​(int n, ContinuousDistribution.Sampler sampler)
    Utility function for allocating an array and filling it with n samples generated by the given sampler.

    Methods inherited from class java.lang.Object

    clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

    Methods inherited from interface org.apache.commons.statistics.distribution.ContinuousDistribution

    probability

  • Constructor Details

    • NormalDistribution

      public NormalDistribution​(double mean, double sd)
      Creates a distribution.
      Parameters:
      mean - Mean for this distribution.
      sd - Standard deviation for this distribution.
      Throws:
      java.lang.IllegalArgumentException - if sd <= 0.

  • Method Details

    • getStandardDeviation

      public double getStandardDeviation()
      Access the standard deviation.
      Returns:
      the standard deviation for this distribution.

    • density

      public double density​(double x)
      Returns the probability density function (PDF) of this distribution evaluated at the specified point x. In general, the PDF is the derivative of the CDF. If the derivative does not exist at x, then an appropriate replacement should be returned, e.g. Double.POSITIVE_INFINITY, Double.NaN, or the limit inferior or limit superior of the difference quotient.
      Parameters:
      x - Point at which the PDF is evaluated.
      Returns:
      the value of the probability density function at x.

    • logDensity

      public double logDensity​(double x)
      Returns the natural logarithm of the probability density function (PDF) of this distribution evaluated at the specified point x.
      Parameters:
      x - Point at which the PDF is evaluated.
      Returns:
      the logarithm of the value of the probability density function at x.

    • cumulativeProbability

      public double cumulativeProbability​(double x)
      For a random variable X whose values are distributed according to this distribution, this method returns P(X <= x). In other words, this method represents the (cumulative) distribution function (CDF) for this distribution. If x is more than 40 standard deviations from the mean, 0 or 1 is returned, as in these cases the actual value is within Double.MIN_VALUE of 0 or 1.
      Parameters:
      x - Point at which the CDF is evaluated.
      Returns:
      the probability that a random variable with this distribution takes a value less than or equal to x.

    • inverseCumulativeProbability

      public double inverseCumulativeProbability​(double p)
      Computes the quantile function of this distribution. For a random variable X distributed according to this distribution, the returned value is
      • inf{x in R | P(X<=x) >= p} for 0 < p <= 1,
      • inf{x in R | P(X<=x) > 0} for p = 0.
      The default implementation returns
      Specified by:
      inverseCumulativeProbability in interface ContinuousDistribution
      Parameters:
      p - Cumulative probability.
      Returns:
      the smallest p-quantile of this distribution (largest 0-quantile for p = 0).

    • probability

      public double probability​(double x0, double x1)
      For a random variable X whose values are distributed according to this distribution, this method returns P(x0 < X <= x1). The default implementation uses the identity P(x0 < X <= x1) = P(X <= x1) - P(X <= x0)
      Parameters:
      x0 - Lower bound (exclusive).
      x1 - Upper bound (inclusive).
      Returns:
      the probability that a random variable with this distribution takes a value between x0 and x1, excluding the lower and including the upper endpoint.

    • getMean

      public double getMean()
      Gets the mean of this distribution.
      Returns:
      the mean, or Double.NaN if it is not defined.

    • getVariance

      public double getVariance()
      Gets the variance of this distribution. For standard deviation parameter s, the variance is s^2.
      Returns:
      the variance, or Double.NaN if it is not defined.

    • getSupportLowerBound

      public double getSupportLowerBound()
      Gets the lower bound of the support. It must return the same value as inverseCumulativeProbability(0), i.e. inf {x in R | P(X <= x) > 0}. The lower bound of the support is always negative infinity no matter the parameters.
      Returns:
      lower bound of the support (always Double.NEGATIVE_INFINITY)

    • getSupportUpperBound

      public double getSupportUpperBound()
      Gets the upper bound of the support. It must return the same value as inverseCumulativeProbability(1), i.e. inf {x in R | P(X <= x) = 1}. The upper bound of the support is always positive infinity no matter the parameters.
      Returns:
      upper bound of the support (always Double.POSITIVE_INFINITY)

    • isSupportConnected

      public boolean isSupportConnected()
      Indicates whether the support is connected, i.e. whether all values between the lower and upper bound of the support are included in the support. The support of this distribution is connected.
      Returns:
      true

    • createSampler

      public ContinuousDistribution.Sampler createSampler​(UniformRandomProvider rng)
      Creates a sampler.
      Specified by:
      createSampler in interface ContinuousDistribution
      Parameters:
      rng - Generator of uniformly distributed numbers.
      Returns:
      a sampler that produces random numbers according this distribution.

    • sample

      public static double[] sample​(int n, ContinuousDistribution.Sampler sampler)
      Utility function for allocating an array and filling it with n samples generated by the given sampler.
      Parameters:
      n - Number of samples.
      sampler - Sampler.
      Returns:
      an array of size n.