Package dev.nm.stat.evt.evd.univariate

Class GeneralizedEVD

    • Constructor Summary

      Constructors 
      Constructor Description
      GeneralizedEVD()
      Create an instance of generalized extreme value distribution with the default parameter values: location \(\mu=0\), scale \(\sigma=1\), shape \(\xi=0\).
      GeneralizedEVD​(double location, double scale, double shape)
      Create an instance of generalized extreme value distribution with the given parameters.

    • Method Summary

      All Methods Instance Methods Concrete Methods 
      Modifier and Type Method Description
      double cdf​(double x)
      Gets the cumulative probability F(x) = Pr(X ≤ x).
      double density​(double x)
      The density function, which, if exists, is the derivative of F.
      double entropy()
      Gets the entropy of this distribution.
      double getLocation()
      Get the location parameter.
      double getScale()
      Get the scale parameter.
      double getShape()
      Get the shape parameter.
      double kurtosis()
      Gets the excess kurtosis of this distribution.
      double logDensity​(double x)
      Get the logarithm of the probability density function at \(x\), that is, \(\log(f(x))\).
      double marginalInverseTransform​(double x)
      Inverse of marginal transform.
      double marginalTransform​(double x)
      Transform to exponential margins under the GEV model.
      double mean()
      Gets the mean of this distribution.
      double median()
      Gets the median of this distribution.
      double moment​(double x)
      The moment generating function is the expected value of etX.
      double quantile​(double p)
      Gets the quantile, the inverse of the cumulative distribution function.
      double skew()
      Gets the skewness of this distribution.
      double variance()
      Gets the variance of this distribution.

    • Constructor Detail

      • GeneralizedEVD

        public GeneralizedEVD()
        Create an instance of generalized extreme value distribution with the default parameter values: location \(\mu=0\), scale \(\sigma=1\), shape \(\xi=0\).

      • GeneralizedEVD

        public GeneralizedEVD​(double location,
                      double scale,
                      double shape)
        Create an instance of generalized extreme value distribution with the given parameters.
        Parameters:
        location - the location parameter \(\mu\)
        scale - the scale parameter \(\sigma > 0\)
        shape - the shape parameter \(\xi\)

    • Method Detail

      • getLocation

        public double getLocation()
        Get the location parameter.
        Returns:
        \(\mu\)

      • getScale

        public double getScale()
        Get the scale parameter.
        Returns:
        \(\sigma\)

      • getShape

        public double getShape()
        Get the shape parameter.
        Returns:
        \(\xi\)

      • marginalTransform

        public double marginalTransform​(double x)
        Transform to exponential margins under the GEV model. That is, /[ t(x) = \begin{cases} \big(1+(\tfrac{x-\mu}{\sigma})\xi\big)^{-1/\xi} \textrm{if}\ \xi\neq0 \\ e^{-(x-\mu)/\sigma} \textrm{if}\ \xi=0 \end{cases} /]
        Parameters:
        x - \(x\)
        Returns:
        \(t(x)\)

      • marginalInverseTransform

        public double marginalInverseTransform​(double x)
        Inverse of marginal transform.
        Parameters:
        x - \(x\)
        Returns:
        \(t^{-1}(x)\)

      • cdf

        public double cdf​(double x)
        Gets the cumulative probability F(x) = Pr(X ≤ x). The cumulative distribution function of GEV distribution is \[ F(x;\mu,\sigma,\xi) = \exp\left\{-\left[1+\xi\left(\frac{x-\mu}{\sigma}\right)\right]^{-1/\xi}\right\} \] for \(1+\xi(x-\mu)/\sigma>0\).
        Specified by:
        cdf in interface ProbabilityDistribution
        Parameters:
        x - \(x\)
        Returns:
        \(F(x)\)
        See Also:
        Wikipedia: Cumulative distribution function

      • density

        public double density​(double x)
        The density function, which, if exists, is the derivative of F. It describes the density of probability at each point in the sample space.
        f(x) = dF(X) / dx
        This may not always exist.

        For the discrete cases, this is the probability mass function. It gives the probability that a discrete random variable is exactly equal to some value. The probability density function of GEV distribution is \[ f(x;\mu,\sigma,\xi) = \frac{1}{\sigma}\left[1+\xi\left(\frac{x-\mu}{\sigma}\right)\right]^{(-1/\xi)-1} \exp\left\{-\left[1+\xi\left(\frac{x-\mu}{\sigma}\right)\right]^{-1/\xi}\right\} \] for \(1+\xi(x-\mu)/\sigma>0\).

        Specified by:
        density in interface ProbabilityDistribution
        Parameters:
        x - \(x\)
        Returns:
        \(f(x)\)
        See Also:

      • logDensity

        public double logDensity​(double x)
        Description copied from interface: UnivariateEVD
        Get the logarithm of the probability density function at \(x\), that is, \(\log(f(x))\).
        Specified by:
        logDensity in interface UnivariateEVD
        Parameters:
        x - \(x\)
        Returns:
        \(\log(f(x))\)

      • quantile

        public double quantile​(double p)
        Description copied from interface: ProbabilityDistribution
        Gets the quantile, the inverse of the cumulative distribution function. It is the value below which random draws from the distribution would fall u×100 percent of the time. 
        
 F-1(u) = x, such that
 Pr(X ≤ x) = u
        This may not always exist.
        Specified by:
        quantile in interface ProbabilityDistribution
        Parameters:
        p - u, a quantile
        Returns:
        F-1(u)
        See Also:
        Wikipedia: Quantile function