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

Class BernoulliDist

  • All Implemented Interfaces:
    Distribution

    public class BernoulliDist
extends DiscreteDistributionInt
    Extends the class DiscreteDistributionInt for the Bernoulli distribution with parameter p, where 0 <= p <= 1. Its mass function is given by

    f (x) = 1 - p,          if x = 0;
    f (x) = p,          if x = 1;
    f (x) = 0,          otherwise.

    Its distribution function is

    F(x) = 0,          if x < 0;
    F(x) = 1 - p,          if 0 <= x < 1;
    F(x) = 1,          if x >= 1.

    • Constructor Summary

      Constructors 
      Constructor and Description
      BernoulliDist(double p)
      Creates a Bernoulli distribution object.

    • Method Summary

      All Methods Static Methods Instance Methods Concrete Methods 
      Modifier and Type Method and Description
      static double barF(double p, int x)
      Returns the complementary Bernoulli distribution function bar(F)(x) = P[X >= x] with parameter p.
      double barF(int x)
      Returns bar(F)(x), the complementary distribution function.
      static double cdf(double p, int x)
      Returns the Bernoulli distribution function F(x) with parameter p (see eq.).
      double cdf(int x)
      Returns the distribution function F evaluated at x (see).
      static BernoulliDist getInstanceFromMLE(int[] x, int m)
      Creates a new instance of a Bernoulli distribution with parameter p estimated using the maximum likelihood method, from the m observations x[i], i = 0, 1,…, m - 1.
      double getMean()
      Returns the mean of the distribution function.
      static double getMean(double p)
      Returns the mean E[X] = p of the Bernoulli distribution with parameter p.
      static double[] getMLE(int[] x, int m)
      Estimates the parameters p of the Bernoulli distribution using the maximum likelihood method, from the m observations x[i], i = 0, 1,…, m - 1.
      double getP()
      Returns the parameter p of this object.
      double[] getParams()
      Returns an array that contains the parameter p of the current distribution: [p].
      double getStandardDeviation()
      Returns the standard deviation of the distribution function.
      static double getStandardDeviation(double p)
      Computes the standard deviation of the Bernoulli distribution with parameter p.
      double getVariance()
      Returns the variance of the distribution function.
      static double getVariance(double p)
      Computes the variance Var[X] = p(1 - p) of the Bernoulli distribution with parameter p.
      static int inverseF(double p, double u)
      Returns the inverse of the Bernoulli distribution function with parameter p at u.
      int inverseFInt(double u)
      Returns the inverse distribution function F-1(u), where 0 <= u <= 1.
      static double prob(double p, int x)
      Returns the Bernoulli probability f (x) with parameter p (see eq.).
      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 p)
      Resets the parameter to this new value.
      java.lang.String toString() 

      • Methods inherited from class java.lang.Object

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

    • Constructor Detail

      • BernoulliDist

        public BernoulliDist(double p)
        Creates a Bernoulli distribution object.

    • 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 p,
                          int x)
        Returns the Bernoulli probability f (x) with parameter p (see eq.).

      • cdf

        public static double cdf(double p,
                         int x)
        Returns the Bernoulli distribution function F(x) with parameter p (see eq.).

      • barF

        public static double barF(double p,
                          int x)
        Returns the complementary Bernoulli distribution function bar(F)(x) = P[X >= x] with parameter p.

      • inverseF

        public static int inverseF(double p,
                           double u)
        Returns the inverse of the Bernoulli distribution function with parameter p at u.

      • getMLE

        public static double[] getMLE(int[] x,
                              int m)
        Estimates the parameters p of the Bernoulli distribution using the maximum likelihood method, from the m observations x[i], i = 0, 1,…, m - 1. The estimate is returned in a one-element array: [p].
        Parameters:
        x - the list of observations used to evaluate parameters
        m - the number of observations used to evaluate parameters
        Returns:
        returns the parameter [hat(p)]

      • getInstanceFromMLE

        public static BernoulliDist getInstanceFromMLE(int[] x,
                                               int m)
        Creates a new instance of a Bernoulli distribution with parameter p estimated using the maximum likelihood method, from the m observations x[i], i = 0, 1,…, m - 1.
        Parameters:
        x - the list of observations to use to estimate the parameters
        m - the number of observations to use to estimate the parameters

      • getMean

        public static double getMean(double p)
        Returns the mean E[X] = p of the Bernoulli distribution with parameter p.
        Returns:
        the mean of the Bernoulli distribution E[X] = np

      • getVariance

        public static double getVariance(double p)
        Computes the variance Var[X] = p(1 - p) of the Bernoulli distribution with parameter p.
        Returns:
        the variance of the Bernoulli distribution

      • getStandardDeviation

        public static double getStandardDeviation(double p)
        Computes the standard deviation of the Bernoulli distribution with parameter p.
        Returns:
        the standard deviation of the Bernoulli distribution

      • getP

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

      • getParams

        public double[] getParams()
        Returns an array that contains the parameter p of the current distribution: [p].

      • setParams

        public void setParams(double p)
        Resets the parameter to this new value.

      • toString

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