Documentation of 'umontreal.iro.lecuyer.probdist.NegativeBinomialDist' Java class
NegativeBinomialDist
Skip navigation links
umontreal.iro.lecuyer.probdist

Class NegativeBinomialDist

  • All Implemented Interfaces:
    Distribution
    Direct Known Subclasses:
    PascalDist

    public class NegativeBinomialDist
extends DiscreteDistributionInt
    Extends the class DiscreteDistributionInt for the negative binomial distribution with real parameters γ and p, where γ > 0 and 0 <= p <= 1. Its mass function is

    p(x) = Γ(γ + x)/(x! Γ(γ))pγ(1 - p)x,        for x = 0, 1, 2,…

    where Γ is the gamma function.

    If γ is an integer, p(x) can be interpreted as the probability of having x failures before the γ-th success in a sequence of independent Bernoulli trials with probability of success p. This special case is implemented as the Pascal distribution (see PascalDist).

    • Constructor Summary

      Constructors 
      Constructor and Description
      NegativeBinomialDist(double gamma, double p)
      Creates an object that contains the probability terms and the distribution function for the negative binomial distribution with parameters γ and p.

    • Method Summary

      All Methods Static Methods Instance Methods Concrete Methods 
      Modifier and Type Method and Description
      double barF(int x)
      Returns bar(F)(x), the complementary distribution function.
      static double cdf(double gamma, double p, int x)
      Computes the distribution function.
      double cdf(int x)
      Returns the distribution function F evaluated at x (see).
      double getGamma()
      Returns the parameter γ of this object.
      static NegativeBinomialDist getInstanceFromMLE(int[] x, int n)
      Creates a new instance of a negative binomial distribution with parameters γ and p estimated using the maximum likelihood method based on the n observations x[i], i = 0, 1,…, n - 1.
      static NegativeBinomialDist getInstanceFromMLE(int[] x, int n, double gamma)
      Creates a new instance of a negative binomial distribution with parameters γ = gamma given and hat(p) estimated using the maximum likelihood method, from the n observations x[i], i = 0, 1,…, n - 1.
      static NegativeBinomialDist getInstanceFromMLE1(int[] x, int n, double p)
      Creates a new instance of a negative binomial distribution with parameters p given and hat(γ) estimated using the maximum likelihood method, from the n observations x[i], i = 0, 1,…, n - 1.
      double getMean()
      Returns the mean of the distribution function.
      static double getMean(double gamma, double p)
      Computes and returns the mean E[X] = γ(1 - p)/p of the negative binomial distribution with parameters γ and p.
      static double[] getMLE(int[] x, int n)
      Estimates the parameter (γ, p) of the negative binomial distribution using the maximum likelihood method, from the n observations x[i], i = 0, 1,…, n - 1.
      static double[] getMLE(int[] x, int n, double gamma)
      Estimates the parameter p of the negative binomial distribution using the maximum likelihood method, from the n observations x[i], i = 0, 1,…, n - 1.
      static double[] getMLE1(int[] x, int n, double p)
      Estimates the parameter γ of the negative binomial distribution using the maximum likelihood method, from the n observations x[i], i = 0, 1,…, n - 1.
      double getP()
      Returns the parameter p of this object.
      double[] getParams()
      Return a table containing the parameters of the current distribution.
      double getStandardDeviation()
      Returns the standard deviation of the distribution function.
      static double getStandardDeviation(double gamma, double p)
      Computes and returns the standard deviation of the negative binomial distribution with parameters γ and p.
      double getVariance()
      Returns the variance of the distribution function.
      static double getVariance(double gamma, double p)
      Computes and returns the variance Var[X] = γ(1 - p)/p2 of the negative binomial distribution with parameters γ and p.
      static int inverseF(double gamma, double p, double u)
      Computes the inverse function without precomputing tables.
      int inverseFInt(double u)
      Returns the inverse distribution function F-1(u), where 0 <= u <= 1.
      static double prob(double gamma, double p, int x)
      Computes the probability p(x).
      double prob(int x)
      Returns p(x), the probability of x, which should be a real number in the interval [0, 1].
      void setParams(double gamma, double p)
      Sets the parameter γ and p of this object.
      java.lang.String toString() 

      • Methods inherited from class java.lang.Object

        equals, getClass, hashCode, notify, notifyAll, wait, wait, wait

    • Field Detail

      • MAXN

        public static double MAXN

    • Constructor Detail

      • NegativeBinomialDist

        public NegativeBinomialDist(double gamma,
                            double p)
        Creates an object that contains the probability terms and the distribution function for the negative binomial distribution with parameters γ and p.

    • Method Detail

      • prob

        public double prob(int x)
        Description copied from class: DiscreteDistributionInt
        Returns p(x), the probability of x, which should be a real number in the interval [0, 1].
        Specified by:
        prob in class DiscreteDistributionInt
        Parameters:
        x - value at which the mass function must be evaluated
        Returns:
        the mass function evaluated at x

      • cdf

        public double cdf(int x)
        Description copied from class: DiscreteDistributionInt
        Returns the distribution function F evaluated at x (see).
        Specified by:
        cdf in class DiscreteDistributionInt
        Parameters:
        x - value at which the distribution function must be evaluated
        Returns:
        the distribution function evaluated at x

      • barF

        public double barF(int x)
        Description copied from class: DiscreteDistributionInt
        Returns bar(F)(x), the complementary distribution function. See the WARNING above.
        Overrides:
        barF in class DiscreteDistributionInt
        Parameters:
        x - value at which the complementary distribution function must be evaluated
        Returns:
        the complementary distribution function evaluated at x

      • inverseFInt

        public int inverseFInt(double u)
        Description copied from class: DiscreteDistributionInt
        Returns the inverse distribution function F-1(u), where 0 <= u <= 1. The default implementation uses binary search.
        Overrides:
        inverseFInt in class DiscreteDistributionInt
        Parameters:
        u - value in the interval (0, 1) for which the inverse distribution function is evaluated
        Returns:
        the inverse distribution function evaluated at u

      • getMean

        public double getMean()
        Description copied from interface: Distribution
        Returns the mean of the distribution function.

      • getVariance

        public double getVariance()
        Description copied from interface: Distribution
        Returns the variance of the distribution function.

      • getStandardDeviation

        public double getStandardDeviation()
        Description copied from interface: Distribution
        Returns the standard deviation of the distribution function.

      • prob

        public static double prob(double gamma,
                          double p,
                          int x)
        Computes the probability p(x).

      • cdf

        public static double cdf(double gamma,
                         double p,
                         int x)
        Computes the distribution function.

      • inverseF

        public static int inverseF(double gamma,
                           double p,
                           double u)
        Computes the inverse function without precomputing tables. This method computes the CDF at the mode (maximum term) and performs a linear search from that point.

      • getMLE

        public static double[] getMLE(int[] x,
                              int n,
                              double gamma)
        Estimates the parameter p of the negative binomial distribution using the maximum likelihood method, from the n observations x[i], i = 0, 1,…, n - 1. The parameter γ = gamma is assumed known. The estimate hat(p) is returned in element 0 of the returned array. The maximum likelihood estimator hat(p) satisfies the equation hat(p) = γ/(γ + bar(x)n), where bar(x)n is the average of x[0],…, x[n - 1].
        Parameters:
        x - the list of observations used to evaluate parameters
        n - the number of observations used to evaluate parameters
        gamma - the first parameter of the negative binomial
        Returns:
        returns the parameters [hat(p)]

      • getInstanceFromMLE

        public static NegativeBinomialDist getInstanceFromMLE(int[] x,
                                                      int n,
                                                      double gamma)
        Creates a new instance of a negative binomial distribution with parameters γ = gamma given and hat(p) estimated using the maximum likelihood method, from the n observations x[i], i = 0, 1,…, n - 1.
        Parameters:
        x - the list of observations to use to evaluate parameters
        n - the number of observations to use to evaluate parameters
        gamma - the first parameter of the negative binomial

      • getMLE1

        public static double[] getMLE1(int[] x,
                               int n,
                               double p)
        Estimates the parameter γ of the negative binomial distribution using the maximum likelihood method, from the n observations x[i], i = 0, 1,…, n - 1. The parameter p is assumed known. The estimate hat(γ) is returned in element 0 of the returned array.
        Parameters:
        x - the list of observations used to evaluate parameters
        n - the number of observations used to evaluate parameters
        p - the second parameter of the negative binomial
        Returns:
        returns the parameters [ hat(γ)]

      • getInstanceFromMLE1

        public static NegativeBinomialDist getInstanceFromMLE1(int[] x,
                                                       int n,
                                                       double p)
        Creates a new instance of a negative binomial distribution with parameters p given and hat(γ) estimated using the maximum likelihood method, from the n observations x[i], i = 0, 1,…, n - 1.
        Parameters:
        x - the list of observations to use to evaluate parameters
        n - the number of observations to use to evaluate parameters
        p - the second parameter of the negative binomial

      • getMLE

        public static double[] getMLE(int[] x,
                              int n)
        Estimates the parameter (γ, p) of the negative binomial distribution using the maximum likelihood method, from the n observations x[i], i = 0, 1,…, n - 1. The estimates are returned in a two-element array, in regular order: [γ, p].
        Parameters:
        x - the list of observations used to evaluate parameters
        n - the number of observations used to evaluate parameters
        Returns:
        returns the parameters [ hat(γ), hat(p)]

      • getInstanceFromMLE

        public static NegativeBinomialDist getInstanceFromMLE(int[] x,
                                                      int n)
        Creates a new instance of a negative binomial distribution with parameters γ and p estimated using the maximum likelihood method based on the n observations x[i], i = 0, 1,…, n - 1.
        Parameters:
        x - the list of observations to use to evaluate parameters
        n - the number of observations to use to evaluate parameters

      • getMean

        public static double getMean(double gamma,
                             double p)
        Computes and returns the mean E[X] = γ(1 - p)/p of the negative binomial distribution with parameters γ and p.
        Returns:
        the mean of the negative binomial distribution E[X] = γ(1 - p)/p

      • getVariance

        public static double getVariance(double gamma,
                                 double p)
        Computes and returns the variance Var[X] = γ(1 - p)/p2 of the negative binomial distribution with parameters γ and p.
        Returns:
        the variance of the negative binomial distribution Var[X] = γ(1 - p)/p2

      • getStandardDeviation

        public static double getStandardDeviation(double gamma,
                                          double p)
        Computes and returns the standard deviation of the negative binomial distribution with parameters γ and p.
        Returns:
        the standard deviation of the negative binomial distribution

      • getGamma

        public double getGamma()
        Returns the parameter γ of this object.

      • getP

        public double getP()
        Returns the parameter p of this object.

      • setParams

        public void setParams(double gamma,
                      double p)
        Sets the parameter γ and p of this object.

      • getParams

        public double[] getParams()
        Return a table containing the parameters of the current distribution. This table is put in regular order: [γ, p].

      • toString

        public java.lang.String toString()
        Overrides:
        toString in class java.lang.Object
Skip navigation links

DMelt 3.0 © DataMelt by jWork.ORG

You see the box below because you did not login.