Package com.imsl.stat.distributions

Class WeibullPD

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

  • Constructor Details

    • WeibullPD

      public WeibullPD()
      Constructor for the Weibull 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 \(k > 0 \) and \(\lambda >0\)

    • 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 \(k > 0 \) and \(\lambda >0\)

    • pdf

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

      The probability density function of the Weibull distribution is $$f\left(x;\lambda,k\right)=\left\{\begin{array} {ll}\frac{k}{\lambda}\left(\frac{x}{\lambda}\right)^{k-1}e^{-\left(x/ \lambda\right)^k} & x\ge 0\\[5pt] 0 & x\lt 0\end{array}\right.$$ where \(k > 0\) is the shape parameter and \(\lambda >0\) is the scale parameter.

      Specified by:
      pdf in class ProbabilityDistribution
      Parameters:
      x - a double, the value (quantile) at which to evaluate the pdf
      params - a double array containing the parameters \(k > 0\) and \(\lambda > 0\). The parameters can also be given in the form pdf(x,a,b), where a=\(k\) 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 \(k > 0\) and \(\lambda > 0\)
      Returns:
      a double array containing the first partial derivative 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 \(k > 0 \) and \(\lambda > 0 \)
      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 the parameters of the Weibull distribution