Package com.imsl.stat.distributions

Class LogLogisticPD

java.lang.Object
com.imsl.stat.distributions.ProbabilityDistribution
com.imsl.stat.distributions.LogLogisticPD
All Implemented Interfaces:
com.imsl.stat.distributions.MethodOfMomentsInterface, PDFGradientInterface, PDFHessianInterface, Serializable, Cloneable
public class LogLogisticPD extends ProbabilityDistribution implements Serializable, Cloneable, PDFHessianInterface, com.imsl.stat.distributions.MethodOfMomentsInterface
The log-logistic probability distribution.
See Also:

  • Constructor Details

    • LogLogisticPD

      public LogLogisticPD()
      Constructor for the log-logistic 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 of length 2 containing the lower bounds for \(\alpha \gt 0\) 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 of length 2 containing the upper bounds for \(\alpha \gt 0\) and \(\beta \gt 0\)

    • pdf

      public double pdf(double x, double... params)
      Returns the value of the log-logistic probability density function.

      The probability density function of the log-logistic distribution is

      $$f(x,\alpha,\beta)=\frac{\beta}{\alpha} \frac{\left( x/\alpha \right )^{\beta - 1}}{\left( 1 + \left( x/\alpha \right )^{\beta} \right)^2}$$

      where \(\alpha \gt 0\) is the scale parameter and \(\beta \gt 0\) is the shape parameter.

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

    • 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 first partial derivatives of the pdf with respect to the parameters

    • getPDFHessian

      public double[][] getPDFHessian(double x, double... params)
      Returns the analytic Hessian 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

    • getMethodOfMomentsEstimates

      public double[] getMethodOfMomentsEstimates(double[] x)
      Returns the method-of-moments estimates given the sample data.
      Specified by:
      getMethodOfMomentsEstimates in interface com.imsl.stat.distributions.MethodOfMomentsInterface
      Parameters:
      x - a double array containing the data
      Returns:
      a double array containing Method of Moments estimates for \(\alpha\) and \(\beta\), the parameters of the log-logistic distribution