Class UniformDiscreteDistribution

java.lang.Object
org.apache.commons.statistics.distribution.AbstractDiscreteDistribution
org.apache.commons.statistics.distribution.UniformDiscreteDistribution
All Implemented Interfaces:
DiscreteDistribution
public final class UniformDiscreteDistribution extends AbstractDiscreteDistribution
Implementation of the uniform discrete distribution.

The probability mass function of \( X \) is:

\[ f(k; a, b) = \frac{1}{b-a+1} \]

for integer \( a, b \) and \( a \le b \) and \( k \in [a, b] \).

See Also:

  • Nested Class Summary

    Nested classes/interfaces inherited from interface DiscreteDistribution

    DiscreteDistribution.Sampler

  • Field Summary

    Fields
    Modifier and Type
    Field
    Description
    private final double
    logPmf
    Cache of the log probability.
    private final int
    lower
    Lower bound (inclusive) of this distribution.
    private final double
    pmf
    Cache of the probability.
    private final double
    sf0
    Value of survival probability for x=0.
    private final int
    upper
    Upper bound (inclusive) of this distribution.
    private final double
    upperMinusLowerPlus1
    "upper" - "lower" + 1 (as a double to avoid overflow).

  • Constructor Summary

    Constructors
    Modifier
    Constructor
    Description
    private
    UniformDiscreteDistribution(int lower, int upper)
     

  • Method Summary

    Modifier and Type
    Method
    Description
    DiscreteDistribution.Sampler
    createSampler(org.apache.commons.rng.UniformRandomProvider rng)
    Creates a sampler.
    double
    cumulativeProbability(int x)
    For a random variable X whose values are distributed according to this distribution, this method returns P(X <= x).
    double
    getMean()
    Gets the mean of this distribution.
    int
    getSupportLowerBound()
    Gets the lower bound of the support.
    int
    getSupportUpperBound()
    Gets the upper bound of the support.
    double
    getVariance()
    Gets the variance of this distribution.
    int
    inverseCumulativeProbability(double p)
    Computes the quantile function of this distribution.
    int
    inverseSurvivalProbability(double p)
    Computes the inverse survival probability function of this distribution.
    double
    logProbability(int x)
    For a random variable X whose values are distributed according to this distribution, this method returns log(P(X = x)), where log is the natural logarithm.
    static UniformDiscreteDistribution
    of(int lower, int upper)
    Creates a new uniform discrete distribution.
    double
    probability(int x)
    For a random variable X whose values are distributed according to this distribution, this method returns P(X = x).
    double
    probability(int x0, int x1)
    For a random variable X whose values are distributed according to this distribution, this method returns P(x0 < X <= x1).
    double
    survivalProbability(int x)
    For a random variable X whose values are distributed according to this distribution, this method returns P(X > x).

    Methods inherited from class AbstractDiscreteDistribution

    getMedian

    Methods inherited from class Object

    clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

  • Field Details

    • lower

      private final int lower
      Lower bound (inclusive) of this distribution.

    • upper

      private final int upper
      Upper bound (inclusive) of this distribution.

    • upperMinusLowerPlus1

      private final double upperMinusLowerPlus1
      "upper" - "lower" + 1 (as a double to avoid overflow).

    • pmf

      private final double pmf
      Cache of the probability.

    • logPmf

      private final double logPmf
      Cache of the log probability.

    • sf0

      private final double sf0
      Value of survival probability for x=0. Used in the inverse survival function.

  • Constructor Details

    • UniformDiscreteDistribution

      private UniformDiscreteDistribution(int lower, int upper)
      Parameters:
      lower - Lower bound (inclusive) of this distribution.
      upper - Upper bound (inclusive) of this distribution.

  • Method Details

    • of

      public static UniformDiscreteDistribution of(int lower, int upper)
      Creates a new uniform discrete distribution.
      Parameters:
      lower - Lower bound (inclusive) of this distribution.
      upper - Upper bound (inclusive) of this distribution.
      Returns:
      the distribution
      Throws:
      IllegalArgumentException - if lower > upper.

    • probability

      public double probability(int x)
      For a random variable X whose values are distributed according to this distribution, this method returns P(X = x). In other words, this method represents the probability mass function (PMF) for the distribution.
      Parameters:
      x - Point at which the PMF is evaluated.
      Returns:
      the value of the probability mass function at x.

    • probability

      public double probability(int x0, int x1)
      For a random variable X whose values are distributed according to this distribution, this method returns P(x0 < X <= x1). The default implementation uses the identity P(x0 < X <= x1) = P(X <= x1) - P(X <= x0)

      Special cases:

      • returns 0.0 if x0 == x1;
      • returns probability(x1) if x0 + 1 == x1;
      Specified by:
      probability in interface DiscreteDistribution
      Overrides:
      probability in class AbstractDiscreteDistribution
      Parameters:
      x0 - Lower bound (exclusive).
      x1 - Upper bound (inclusive).
      Returns:
      the probability that a random variable with this distribution takes a value between x0 and x1, excluding the lower and including the upper endpoint.

    • logProbability

      public double logProbability(int x)
      For a random variable X whose values are distributed according to this distribution, this method returns log(P(X = x)), where log is the natural logarithm.
      Parameters:
      x - Point at which the PMF is evaluated.
      Returns:
      the logarithm of the value of the probability mass function at x.

    • cumulativeProbability

      public double cumulativeProbability(int x)
      For a random variable X whose values are distributed according to this distribution, this method returns P(X <= x). In other, words, this method represents the (cumulative) distribution function (CDF) for this distribution.
      Parameters:
      x - Point at which the CDF is evaluated.
      Returns:
      the probability that a random variable with this distribution takes a value less than or equal to x.

    • survivalProbability

      public double survivalProbability(int x)
      For a random variable X whose values are distributed according to this distribution, this method returns P(X > x). In other words, this method represents the complementary cumulative distribution function.

      By default, this is defined as 1 - cumulativeProbability(x), but the specific implementation may be more accurate.

      Parameters:
      x - Point at which the survival function is evaluated.
      Returns:
      the probability that a random variable with this distribution takes a value greater than x.

    • inverseCumulativeProbability

      public int inverseCumulativeProbability(double p)
      Computes the quantile function of this distribution. For a random variable X distributed according to this distribution, the returned value is:

      \[ x = \begin{cases} \inf \{ x \in \mathbb Z : P(X \le x) \ge p\} & \text{for } 0 \lt p \le 1 \\ \inf \{ x \in \mathbb Z : P(X \le x) \gt 0 \} & \text{for } p = 0 \end{cases} \]

      If the result exceeds the range of the data type int, then Integer.MIN_VALUE or Integer.MAX_VALUE is returned. In this case the result of cumulativeProbability(x) called using the returned p-quantile may not compute the original p.

      The default implementation returns:

      Specified by:
      inverseCumulativeProbability in interface DiscreteDistribution
      Overrides:
      inverseCumulativeProbability in class AbstractDiscreteDistribution
      Parameters:
      p - Cumulative probability.
      Returns:
      the smallest p-quantile of this distribution (largest 0-quantile for p = 0).

    • inverseSurvivalProbability

      public int inverseSurvivalProbability(double p)
      Computes the inverse survival probability function of this distribution. For a random variable X distributed according to this distribution, the returned value is:

      \[ x = \begin{cases} \inf \{ x \in \mathbb Z : P(X \gt x) \le p\} & \text{for } 0 \le p \lt 1 \\ \inf \{ x \in \mathbb Z : P(X \gt x) \lt 1 \} & \text{for } p = 1 \end{cases} \]

      If the result exceeds the range of the data type int, then Integer.MIN_VALUE or Integer.MAX_VALUE is returned. In this case the result of survivalProbability(x) called using the returned (1-p)-quantile may not compute the original p.

      By default, this is defined as inverseCumulativeProbability(1 - p), but the specific implementation may be more accurate.

      The default implementation returns:

      Specified by:
      inverseSurvivalProbability in interface DiscreteDistribution
      Overrides:
      inverseSurvivalProbability in class AbstractDiscreteDistribution
      Parameters:
      p - Cumulative probability.
      Returns:
      the smallest (1-p)-quantile of this distribution (largest 0-quantile for p = 1).

    • getMean

      public double getMean()
      Gets the mean of this distribution.

      For lower bound \( a \) and upper bound \( b \), the mean is \( \frac{1}{2} (a + b) \).

      Returns:
      the mean.

    • getVariance

      public double getVariance()
      Gets the variance of this distribution.

      For lower bound \( a \) and upper bound \( b \), the variance is:

      \[ \frac{1}{12} (n^2 - 1) \]

      where \( n = b - a + 1 \).

      Returns:
      the variance.

    • getSupportLowerBound

      public int getSupportLowerBound()
      Gets the lower bound of the support. This method must return the same value as inverseCumulativeProbability(0), i.e. \( \inf \{ x \in \mathbb Z : P(X \le x) \gt 0 \} \). By convention, Integer.MIN_VALUE should be substituted for negative infinity.

      The lower bound of the support is equal to the lower bound parameter of the distribution.

      Returns:
      the lower bound of the support.

    • getSupportUpperBound

      public int getSupportUpperBound()
      Gets the upper bound of the support. This method must return the same value as inverseCumulativeProbability(1), i.e. \( \inf \{ x \in \mathbb Z : P(X \le x) = 1 \} \). By convention, Integer.MAX_VALUE should be substituted for positive infinity.

      The upper bound of the support is equal to the upper bound parameter of the distribution.

      Returns:
      the upper bound of the support.

    • createSampler

      public DiscreteDistribution.Sampler createSampler(org.apache.commons.rng.UniformRandomProvider rng)
      Creates a sampler.
      Specified by:
      createSampler in interface DiscreteDistribution
      Overrides:
      createSampler in class AbstractDiscreteDistribution
      Parameters:
      rng - Generator of uniformly distributed numbers.
      Returns:
      a sampler that produces random numbers according this distribution.