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

Class UniformIntDist

  • All Implemented Interfaces:
    Distribution

    public class UniformIntDist
extends DiscreteDistributionInt
    Extends the class DiscreteDistributionInt for the discrete uniform distribution over the range [i, j]. Its mass function is given by

    p(x) = 1/(j - i + 1)         for x = i, i + 1,…, j

    and 0 elsewhere. The distribution function is

    F(x) = (floor(x) - i + 1)/(j - i + 1)         for i <= x <= j

    and its inverse is

    F-1(u) = i + (j - i + 1)u        for 0 <= u <= 1.

    • Constructor Summary

      Constructors 
      Constructor and Description
      UniformIntDist(int i, int j)
      Constructs a discrete uniform distribution over the interval [i, j].

    • 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 barF(int i, int j, int x)
      Computes the discrete uniform complementary distribution function bar(F)(x).
      double cdf(int x)
      Returns the distribution function F evaluated at x (see).
      static double cdf(int i, int j, int x)
      Computes the discrete uniform distribution function defined in.
      int getI()
      Returns the parameter i.
      static UniformIntDist getInstanceFromMLE(int[] x, int n)
      Creates a new instance of a discrete uniform distribution over integers with parameters i and j estimated using the maximum likelihood method based on the n observations x[k], k = 0, 1,…, n - 1.
      int getJ()
      Returns the parameter j.
      double getMean()
      Returns the mean of the distribution function.
      static double getMean(int i, int j)
      Computes and returns the mean E[X] = (i + j)/2 of the discrete uniform distribution.
      static double[] getMLE(int[] x, int n)
      Estimates the parameters (i, j) of the uniform distribution over integers using the maximum likelihood method, from the n observations x[k], k = 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(int i, int j)
      Computes and returns the standard deviation of the discrete uniform distribution.
      double getVariance()
      Returns the variance of the distribution function.
      static double getVariance(int i, int j)
      Computes and returns the variance Var[X] = [(j - i + 1)2 -1]/12 of the discrete uniform distribution.
      static int inverseF(int i, int j, double u)
      Computes the inverse of the discrete uniform distribution function.
      int inverseFInt(double u)
      Returns the inverse distribution function F-1(u), where 0 <= u <= 1.
      double prob(int x)
      Returns p(x), the probability of x, which should be a real number in the interval [0, 1].
      static double prob(int i, int j, int x)
      Computes the discrete uniform probability p(x).
      void setParams(int i, int j)
      Sets the parameters i and j for this object.
      java.lang.String toString() 

      • Methods inherited from class java.lang.Object

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

    • Constructor Detail

      • UniformIntDist

        public UniformIntDist(int i,
                      int j)
        Constructs a discrete uniform distribution over the interval [i, j].

    • 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(int i,
                          int j,
                          int x)
        Computes the discrete uniform probability p(x).

      • cdf

        public static double cdf(int i,
                         int j,
                         int x)
        Computes the discrete uniform distribution function defined in.

      • barF

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

      • inverseF

        public static int inverseF(int i,
                           int j,
                           double u)
        Computes the inverse of the discrete uniform distribution function.

      • getMLE

        public static double[] getMLE(int[] x,
                              int n)
        Estimates the parameters (i, j) of the uniform distribution over integers using the maximum likelihood method, from the n observations x[k], k = 0, 1,…, n - 1. The estimates are returned in a two-element array, in regular order: [i, j].
        Parameters:
        x - the list of observations used to evaluate parameters
        n - the number of observations used to evaluate parameters
        Returns:
        returns the parameters [ hat(ı), hat(&jnodot;)]

      • getInstanceFromMLE

        public static UniformIntDist getInstanceFromMLE(int[] x,
                                                int n)
        Creates a new instance of a discrete uniform distribution over integers with parameters i and j estimated using the maximum likelihood method based on the n observations x[k], k = 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(int i,
                             int j)
        Computes and returns the mean E[X] = (i + j)/2 of the discrete uniform distribution.
        Returns:
        the mean of the discrete uniform distribution

      • getVariance

        public static double getVariance(int i,
                                 int j)
        Computes and returns the variance Var[X] = [(j - i + 1)2 -1]/12 of the discrete uniform distribution.
        Returns:
        the variance of the discrete uniform distribution

      • getStandardDeviation

        public static double getStandardDeviation(int i,
                                          int j)
        Computes and returns the standard deviation of the discrete uniform distribution.
        Returns:
        the standard deviation of the discrete uniform distribution

      • getI

        public int getI()
        Returns the parameter i.

      • getJ

        public int getJ()
        Returns the parameter j.

      • setParams

        public void setParams(int i,
                      int j)
        Sets the parameters i and j for this object.

      • getParams

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

      • toString

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