Package com.imsl.stat.distributions

Class InverseGaussianPD

java.lang.Object
com.imsl.stat.distributions.ProbabilityDistribution
com.imsl.stat.distributions.InverseGaussianPD
All Implemented Interfaces:
ClosedFormMaximumLikelihoodInterface, PDFGradientInterface, PDFHessianInterface, Serializable, Cloneable
public class InverseGaussianPD extends ProbabilityDistribution implements PDFHessianInterface, ClosedFormMaximumLikelihoodInterface, Serializable, Cloneable
The inverse Gaussian (Wald) probability distribution.
See Also:

  • Constructor Details

    • InverseGaussianPD

      public InverseGaussianPD()
      Constructor for the inverse 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 \(\mu \gt 0\) and \(\lambda \gt 0\)

    • 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 \(\mu \gt 0\) and \(\lambda \gt 0\)

    • pdf

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

      The probability density function for an inverse Gaussian distribution is given by $$f(x; \mu,\lambda) = \sqrt{\frac{\lambda}{2 \pi x^3}} \exp^{-\frac{\lambda (x - \mu)^2}{2 \mu^2 x}} $$ where \(\mu > 0\) and \(\lambda > 0\) are the mean and shape of the random variable.

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

    • getPDFGradient

      public double[] getPDFGradient(double x, double... params)
      Returns the analytic gradient of the pdf.
      Specified by:
      getPDFGradient in interface PDFGradientInterface
      Parameters:
      x - a double, the value at which to evaluate the gradient
      params - a double array containing the parameters
      Returns:
      a double array containing the partial derivatives of the pdf with respect to the parameters

    • getPDFHessian

      public double[][] getPDFHessian(double x, double... params)
      Returns the analytic Hessian matrix of the pdf.
      Specified by:
      getPDFHessian in interface PDFHessianInterface
      Parameters:
      x - a double, the value at which to evaluate the Hessian
      params - a double array containing the parameters
      Returns:
      a double matrix containing the second partial derivatives of the pdf with respect to the parameters

    • getClosedFormMLE

      public double[] getClosedFormMLE(double[] x)
      Returns the closed form maximum likelihood estimates.
      Specified by:
      getClosedFormMLE in interface ClosedFormMaximumLikelihoodInterface
      Parameters:
      x - a double array containing the data
      Returns:
      a double array containing the maximum likelihood estimates for \(\mu\) and \(\lambda\)

    • getClosedFormMlStandardError

      public double[] getClosedFormMlStandardError(double[] x)
      Returns the standard errors of the closed form maximum likelihood estimates.
      Specified by:
      getClosedFormMlStandardError in interface ClosedFormMaximumLikelihoodInterface
      Parameters:
      x - a double array containing the data
      Returns:
      a double array containing the standard errors for the estimates of \(\mu\) and \(\lambda\)