Package org.apache.commons.math3.distribution

Class GumbelDistribution

java.lang.Object
org.apache.commons.math3.distribution.AbstractRealDistribution
org.apache.commons.math3.distribution.GumbelDistribution
All Implemented Interfaces:
Serializable, RealDistribution
public class GumbelDistribution extends AbstractRealDistribution
This class implements the Gumbel distribution.
Since:
3.4
See Also:

  • Constructor Details

    • GumbelDistribution

      public GumbelDistribution(double mu, double beta)
      Build a new instance.

      Note: this constructor will implicitly create an instance of Well19937c as random generator to be used for sampling only (see AbstractRealDistribution.sample() and AbstractRealDistribution.sample(int)). In case no sampling is needed for the created distribution, it is advised to pass null as random generator via the appropriate constructors to avoid the additional initialisation overhead.

      Parameters:
      mu - location parameter
      beta - scale parameter (must be positive)
      Throws:
      NotStrictlyPositiveException - if beta <= 0

    • GumbelDistribution

      public GumbelDistribution(RandomGenerator rng, double mu, double beta)
      Build a new instance.
      Parameters:
      rng - Random number generator
      mu - location parameter
      beta - scale parameter (must be positive)
      Throws:
      NotStrictlyPositiveException - if beta <= 0

  • Method Details

    • getLocation

      public double getLocation()
      Access the location parameter, mu.
      Returns:
      the location parameter.

    • getScale

      public double getScale()
      Access the scale parameter, beta.
      Returns:
      the scale parameter.

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

      public double inverseCumulativeProbability(double p) throws OutOfRangeException
      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(Xinvalid input: '<'=x) >= p} for 0 < p <= 1,
      • inf{x in R | P(Xinvalid input: '<'=x) > 0} for p = 0.
      The default implementation returns
      Specified by:
      inverseCumulativeProbability in interface RealDistribution
      Overrides:
      inverseCumulativeProbability in class AbstractRealDistribution
      Parameters:
      p - the cumulative probability
      Returns:
      the smallest p-quantile of this distribution (largest 0-quantile for p = 0)
      Throws:
      OutOfRangeException - if p < 0 or p > 1

    • getNumericalMean

      public 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

      public 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

      public 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 invalid input: '<'= x) > 0}.

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

    • getSupportUpperBound

      public 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 invalid input: '<'= x) = 1}.

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

    • isSupportLowerBoundInclusive

      public boolean isSupportLowerBoundInclusive()
      Whether or not the lower bound of support is in the domain of the density function. Returns true iff getSupporLowerBound() is finite and density(getSupportLowerBound()) returns a non-NaN, non-infinite value.
      Returns:
      true if the lower bound of support is finite and the density function returns a non-NaN, non-infinite value there

    • isSupportUpperBoundInclusive

      public boolean isSupportUpperBoundInclusive()
      Whether or not the upper bound of support is in the domain of the density function. Returns true iff getSupportUpperBound() is finite and density(getSupportUpperBound()) returns a non-NaN, non-infinite value.
      Returns:
      true if the upper bound of support is finite and the density function returns a non-NaN, non-infinite value there

    • isSupportConnected

      public 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