Documentation of 'umontreal.iro.lecuyer.probdist.LogarithmicDist' Java class
LogarithmicDist
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umontreal.iro.lecuyer.probdist

Class LogarithmicDist

  • All Implemented Interfaces:
    Distribution

    public class LogarithmicDist
extends DiscreteDistributionInt
    Extends the class DiscreteDistributionInt for the logarithmic distribution. It has shape parameter θ, where 0 < θ < 1. Its mass function is

    p(x) = - θx/(x log(1 - θ)        for x = 1, 2, 3,...

    Its distribution function is

    F(x) = -1/log(1-θ)∑i=1xθi/i, & for x > 0.

    • Constructor Summary

      Constructors 
      Constructor and Description
      LogarithmicDist(double theta)
      Constructs a logarithmic distribution with parameter θ = theta.

    • Method Summary

      All Methods Static Methods Instance Methods Concrete Methods 
      Modifier and Type Method and Description
      static double barF(double theta, int x)
      Computes the complementary distribution function.
      double barF(int x)
      Returns bar(F)(x), the complementary distribution function.
      static double cdf(double theta, int x)
      Computes the distribution function F(x).
      double cdf(int x)
      Returns the distribution function F evaluated at x (see).
      static LogarithmicDist getInstanceFromMLE(int[] x, int n)
      Creates a new instance of a logarithmic distribution with parameter θ estimated using the maximum likelihood method based on the n observations x[i], i = 0, 1,…, n - 1.
      double getMean()
      Returns the mean of the distribution function.
      static double getMean(double theta)
      Computes and returns the mean of the logarithmic distribution with parameter θ = theta.
      static double[] getMLE(int[] x, int n)
      Estimates the parameter θ of the logarithmic distribution using the maximum likelihood method, from the n observations x[i], i = 0, 1,…, n - 1.
      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 theta)
      Computes and returns the standard deviation of the logarithmic distribution with parameter θ = theta.
      double getTheta()
      Returns the θ associated with this object.
      double getVariance()
      Returns the variance of the distribution function.
      static double getVariance(double theta)
      Computes and returns the variance of the logarithmic distribution with parameter θ = theta.
      static int inverseF(double theta, double u) 
      int inverseFInt(double u)
      Returns the inverse distribution function F-1(u), where 0 <= u <= 1.
      static double prob(double theta, int x)
      Computes the logarithmic 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 setTheta(double theta)
      Sets the θ associated with this object.
      java.lang.String toString() 

      • Methods inherited from class java.lang.Object

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

    • Constructor Detail

      • LogarithmicDist

        public LogarithmicDist(double theta)
        Constructs a logarithmic distribution with parameter θ = theta.

    • 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 theta,
                          int x)
        Computes the logarithmic probability p(x).

      • cdf

        public static double cdf(double theta,
                         int x)
        Computes the distribution function F(x).

      • barF

        public static double barF(double theta,
                          int x)
        Computes the complementary distribution function. WARNING: The complementary distribution function is defined as bar(F)(x) = P[X >= x].

      • inverseF

        public static int inverseF(double theta,
                           double u)

      • getMLE

        public static double[] getMLE(int[] x,
                              int n)
        Estimates the parameter θ of the logarithmic distribution using the maximum likelihood method, from the n observations x[i], i = 0, 1,…, n - 1. The estimate 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
        Returns:
        returns the parameter [ hat(&thetas;)]

      • getInstanceFromMLE

        public static LogarithmicDist getInstanceFromMLE(int[] x,
                                                 int n)
        Creates a new instance of a logarithmic distribution with parameter θ 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 theta)
        Computes and returns the mean of the logarithmic distribution with parameter θ = theta.
        Returns:
        the mean of the logarithmic distribution E[X] = - θ/((1 - θ)ln(1 - θ))

      • getVariance

        public static double getVariance(double theta)
        Computes and returns the variance of the logarithmic distribution with parameter θ = theta.
        Returns:
        the variance of the logarithmic distribution Var[X] = - θ(θ + ln(1 - θ))/((1 - θ)2(ln(1 - θ))2)

      • getStandardDeviation

        public static double getStandardDeviation(double theta)
        Computes and returns the standard deviation of the logarithmic distribution with parameter θ = theta.
        Returns:
        the standard deviation of the logarithmic distribution

      • getTheta

        public double getTheta()
        Returns the θ associated with this object.

      • setTheta

        public void setTheta(double theta)
        Sets the θ associated with this object.

      • getParams

        public double[] getParams()
        Return a table containing the parameters of the current distribution.

      • toString

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