Package com.imsl.stat.distributions

Class RayleighPD

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

  • Constructor Details

    • RayleighPD

      public RayleighPD()
      Constructor for the Rayleigh probability distribution.

  • Method Details

    • getParameterLowerBounds

      public double[] getParameterLowerBounds()
      Returns the lower bound for the parameter.
      Specified by:
      getParameterLowerBounds in class ProbabilityDistribution
      Returns:
      a double array of length 1 containing the lower bound for \(\sigma>0\)

    • getParameterUpperBounds

      public double[] getParameterUpperBounds()
      Returns the upper bound for the parameter.
      Specified by:
      getParameterUpperBounds in class ProbabilityDistribution
      Returns:
      a double array of length 1 containing the upper bound for \(\sigma>0\)

    • pdf

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

      The probability density function of the Rayleigh distribution is $$f\left(x;\sigma\right)=\begin{array}{ll} \frac{x}{\sigma^2}e^{-x^2/\left(2\sigma^2\right)}, & x\ge0 \end{array}$$ where \(\sigma > 0\) 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, the scale parameter (\(\sigma\gt 0\))
      Returns:
      a double, the probability density at x given the parameter value

    • 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. x must be non-negative.
      params - a double, the scale parameter (\(\sigma\gt 0\))
      Returns:
      a double array containing the first partial derivative of the pdf with respect to the parameter

    • 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. x must be non-negative.
      params - a double, the scale parameter (\(\sigma\gt 0\))
      Returns:
      a double matrix containing the second partial derivatives of the pdf with respect to the parameter

    • getClosedFormMLE

      public double[] getClosedFormMLE(double[] x)
      Returns the closed form maximum likelihood estimate.
      Specified by:
      getClosedFormMLE in interface ClosedFormMaximumLikelihoodInterface
      Parameters:
      x - a double array containing the data
      Returns:
      a double array containing the maximum likelihood estimate

    • getClosedFormMlStandardError

      public double[] getClosedFormMlStandardError(double[] x)
      Returns the standard error based on the closed form maximum likelihood estimate.
      Specified by:
      getClosedFormMlStandardError in interface ClosedFormMaximumLikelihoodInterface
      Parameters:
      x - a double array containing the data
      Returns:
      a double array containing the standard error

    • getMethodOfMomentsEstimates

      public double[] getMethodOfMomentsEstimates(double[] x)
      Returns the method-of-moments estimate 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 estimate for the parameter