Package com.imsl.stat.distributions

Class NegativeBinomialPD

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

  • Constructor Details

    • NegativeBinomialPD

      public NegativeBinomialPD()
      Constructor for the binomial 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 \(p\)

    • 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 \(p\)

    • pdf

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

      The probability density function of the negative binomial distribution is

      $$\Pr \left( {X = k} \right) = {k+r-1 \choose r - 1} p^r (1-p)^k, \quad r =1, 2, \ldots, \; k = 0, 1,2, \ldots $$

      where \(k\) is the number of failures before obtaining \(r\) successes, and \(p \in [0,1]\) is the success probability in each independent trial.

      Specified by:
      pdf in class ProbabilityDistribution
      Parameters:
      x - a double, the number of failures before obtaining r successes. x must be a non-negative integer. If x is not an integer, then it is cast to an integer. The number of successes can be set via method setNumberOfSuccesses(int).
      params - a double scalar value representing the probability of success on each independent trial, \(p\)
      Returns:
      a double, the probability density at x given the parameter value, \(p\)

    • 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 an integer, then x is cast to an integer.
      params - a double, the value of the parameter \(p\)
      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 an integer, the integer cast value will be used.
      params - a double, the value of the parameter \(p\)
      Returns:
      a double matrix containing the second partial derivative 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

    • setNumberOfSuccesses

      public void setNumberOfSuccesses(int numSuccesses)
      Sets the number of successes.
      Parameters:
      numSuccesses - an int, the number of successes. The default is numSuccesses=1.

    • getNumberOfSuccesses

      public int getNumberOfSuccesses()
      Returns the number of successes.
      Returns:
      an int, the number of successes set