Package com.imsl.stat.distributions

Class GeneralizedGaussianPD

java.lang.Object
com.imsl.stat.distributions.ProbabilityDistribution
com.imsl.stat.distributions.GeneralizedGaussianPD
All Implemented Interfaces:
com.imsl.stat.distributions.MethodOfMomentsInterface, Serializable, Cloneable
public class GeneralizedGaussianPD extends ProbabilityDistribution implements Serializable, Cloneable, com.imsl.stat.distributions.MethodOfMomentsInterface
The generalized Gaussian probability distribution.
See Also:

  • Constructor Details

    • GeneralizedGaussianPD

      public GeneralizedGaussianPD()
      Constructs a generalized Gaussian probability distribution.

  • Method Details

    • getParameterLowerBounds

      public double[] getParameterLowerBounds()
      Returns the lower bounds of the parameters.
      Specified by:
      getParameterLowerBounds in class ProbabilityDistribution
      Returns:
      a double array containing the lower bounds for \(\mu\in\mathbb{R}\), \(\alpha \gt 0\), and \(\beta \gt 0\)

    • getParameterUpperBounds

      public double[] getParameterUpperBounds()
      Returns the upper bounds of the parameters.
      Specified by:
      getParameterUpperBounds in class ProbabilityDistribution
      Returns:
      a double array containing the upper bounds for \(\mu\in\mathbb{R}\), \(\alpha \gt 0\), and \(\beta \gt 0\)

    • pdf

      public double pdf(double x, double... params)
      Returns the value of the generalized Gaussian probability density function.

      The probability density function of the generalized Gaussian distribution is

      $$ f(x; \mu,\alpha, \beta) = \frac{\beta}{2\alpha\Gamma(\frac{1}{\beta})} e^{-(\frac{|x-\mu|}{\alpha})^\beta} $$

      where \(\mu\in\mathbb{R}\) is the location parameter, \(\alpha \gt 0\) is the scale parameter, and \(\beta \gt 0\) is the shape parameter. Note that this follows the parameterization given in Wikipedia. There are alternative parameterizations, as in Roenko, et. al. 2014.

      References
      1. Roenko, Alexey, Lukin, Vladimir, Djurovic, Igor, Simeunović, Marko. (2014). Estimation of parameters for generalized Gaussian distribution. ISCCSP 2014 - 2014 6th International Symposium on Communications, Control and Signal Processing, Proceedings. 376-379.
      2. Wikipedia contributors. "Generalized normal distribution." Wikipedia, The Free Encyclopedia.

      Specified by:
      pdf in class ProbabilityDistribution
      Parameters:
      x - a double, the value (quantile) at which to evaluate the pdf
      params - a double array containing \(\mu\), \(\alpha\), and \(\beta\). The parameters can also be given in the form pdf(x,a,b,c), where a=\(\mu\), b=\(\alpha\), and c=\(\beta\) are scalars.
      Returns:
      a double, the probability density at x given the parameter values