Package com.imsl.stat.distributions

Class PoissonPD

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

  • Constructor Details

    • PoissonPD

      public PoissonPD()
      Constructor for the Poisson probability distribution.

  • Method Details

    • getParameterLowerBounds

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

    • getParameterUpperBounds

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

    • pdf

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

      The probability density function of the Poisson distribution is $$\begin{array}{ll}f(k|\theta)=e^{-\theta}\theta^k/k! & \mbox{for}\;k=0, 1, 2, \ldots\end{array}$$

      Specified by:
      pdf in class ProbabilityDistribution
      Parameters:
      x - a double, the value (quantile) at which to evaluate the pdf. x must be a non-negative integer. If x is not a whole number the floor() value will be used.
      params - a double specifying the parameter, \(\theta\)
      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 pdf. x must be a non-negative integer. If x is not a whole number the floor() value will be used.
      params - a double, the value of the parameter \(\theta\)
      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 a non-negative integer. If x is not a whole number the floor() value will be used.
      params - a double, the value of the parameter \(\theta\)
      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 of the Poisson distribution