Package org.hipparchus.distribution

Interface RealDistribution

All Known Implementing Classes:
AbstractRealDistribution, BetaDistribution, CauchyDistribution, ChiSquaredDistribution, ConstantRealDistribution, EnumeratedRealDistribution, ExponentialDistribution, FDistribution, GammaDistribution, GumbelDistribution, LaplaceDistribution, LevyDistribution, LogisticDistribution, LogNormalDistribution, NakagamiDistribution, NormalDistribution, ParetoDistribution, TDistribution, TriangularDistribution, UniformRealDistribution, WeibullDistribution
public interface RealDistribution
Base interface for continuous distributions.

  • Method Summary

    Modifier and Type
    Method
    Description
    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
    getNumericalMean()
    Use this method to get the numerical value of the mean of this distribution.
    double
    getNumericalVariance()
    Use this method to get the numerical value of the variance of this distribution.
    double
    getSupportLowerBound()
    Access the lower bound of the support.
    double
    getSupportUpperBound()
    Access the upper bound of the support.
    double
    inverseCumulativeProbability(double p)
    Computes the quantile function of this distribution.
    boolean
    isSupportConnected()
    Use this method to get information about 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).

  • Method Details

    • probability

      double probability(double x0, double x1) throws MathIllegalArgumentException
      For a random variable X whose values are distributed according to this distribution, this method returns P(x0 < X <= x1).
      Parameters:
      x0 - the exclusive lower bound
      x1 - the inclusive upper bound
      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
      Throws:
      MathIllegalArgumentException - if x0 > x1

    • density

      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 - the point at which the PDF is evaluated
      Returns:
      the value of the probability density function at point x

    • logDensity

      double logDensity(double x)
      Returns the natural logarithm of 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. Note that due to the floating point precision and under/overflow issues, this method will for some distributions be more precise and faster than computing the logarithm of density(double).
      Parameters:
      x - the point at which the PDF is evaluated
      Returns:
      the logarithm of the value of the probability density function at point x

    • cumulativeProbability

      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.
      Parameters:
      x - the 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

      double inverseCumulativeProbability(double p) throws MathIllegalArgumentException
      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.
      Parameters:
      p - the cumulative probability
      Returns:
      the smallest p-quantile of this distribution (largest 0-quantile for p = 0)
      Throws:
      MathIllegalArgumentException - if p < 0 or p > 1

    • getNumericalMean

      double getNumericalMean()
      Use this method to get the numerical value of the mean of this distribution.
      Returns:
      the mean or Double.NaN if it is not defined

    • getNumericalVariance

      double getNumericalVariance()
      Use this method to get the numerical value of the variance of this distribution.
      Returns:
      the variance (possibly Double.POSITIVE_INFINITY as for certain cases in TDistribution) or Double.NaN if it is not defined

    • getSupportLowerBound

      double getSupportLowerBound()
      Access the lower bound of the support. This method must return the same value as inverseCumulativeProbability(0). In other words, this method must return

      inf {x in R | P(X <= x) > 0}.

      Returns:
      lower bound of the support (might be Double.NEGATIVE_INFINITY)

    • getSupportUpperBound

      double getSupportUpperBound()
      Access the upper bound of the support. This method must return the same value as inverseCumulativeProbability(1). In other words, this method must return

      inf {x in R | P(X <= x) = 1}.

      Returns:
      upper bound of the support (might be Double.POSITIVE_INFINITY)

    • isSupportConnected

      boolean isSupportConnected()
      Use this method to get information about whether the support is connected, i.e. whether all values between the lower and upper bound of the support are included in the support.
      Returns:
      whether the support is connected or not