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## org.apache.commons.math.distribution
Class AbstractIntegerDistribution

    java.lang.Object
      org.apache.commons.math.distribution.AbstractDistribution
          org.apache.commons.math.distribution.AbstractIntegerDistribution

All Implemented Interfaces:
  java.io.Serializable, DiscreteDistribution, Distribution, IntegerDistribution

Direct Known Subclasses:
  BinomialDistributionImpl, HypergeometricDistributionImpl, PascalDistributionImpl, PoissonDistributionImpl, ZipfDistributionImpl

    public abstract class AbstractIntegerDistribution

extends AbstractDistribution
implements IntegerDistribution, java.io.Serializable

Base class for integer-valued discrete distributions. Default implementations are provided for some of the methods that do not vary from distribution to distribution.

Version:
  $Revision: 920558 $ $Date: 2010-03-08 17:57:32 -0500 (Mon, 08 Mar 2010) $
See Also:
  Serialized Form

Field Summary
`private static java.lang.String` | `OUT_OF_RANGE_POINT` Message for out of range point.
`private static long` | `serialVersionUID` Serializable version identifier
`private static java.lang.String` | `WRONG_ORDER_ENDPOINTS_MESSAGE` Message for endpoints in wrong order.

Constructor Summary
`protected` | `AbstractIntegerDistribution()` Default constructor.

Method Summary
`private double` | `checkedCumulativeProbability(int argument)` Computes the cumulative probablity function and checks for NaN values returned.
`double` | `cumulativeProbability(double x)` For a random variable X whose values are distributed according to this distribution, this method returns P(X ≤ x).
`double` | `cumulativeProbability(double x0, double x1)` For a random variable X whose values are distributed according to this distribution, this method returns P(x0 ≤ X ≤ x1).
`abstract double` | `cumulativeProbability(int x)` For a random variable X whose values are distributed according to this distribution, this method returns P(X ≤ x).
`double` | `cumulativeProbability(int x0, int x1)` For a random variable X whose values are distributed according to this distribution, this method returns P(x0 ≤ X ≤ x1).
`protected abstract int` | `getDomainLowerBound(double p)` Access the domain value lower bound, based on `p`, used to bracket a PDF root.
`protected abstract int` | `getDomainUpperBound(double p)` Access the domain value upper bound, based on `p`, used to bracket a PDF root.
`int` | `inverseCumulativeProbability(double p)` For a random variable X whose values are distributed according to this distribution, this method returns the largest x, such that P(X ≤ x) ≤ `p`.
`double` | `probability(double x)` For a random variable X whose values are distributed according to this distribution, this method returns P(X = x).

Methods inherited from class java.lang.Object
`clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait`

Methods inherited from interface org.apache.commons.math.distribution.IntegerDistribution
`probability`

Field Detail

### WRONG_ORDER_ENDPOINTS_MESSAGE

    private static final java.lang.String WRONG_ORDER_ENDPOINTS_MESSAGE

  Message for endpoints in wrong order.

  See Also:
    Constant Field Values

### OUT_OF_RANGE_POINT

    private static final java.lang.String OUT_OF_RANGE_POINT

  Message for out of range point.

  See Also:
    Constant Field Values

### serialVersionUID

    private static final long serialVersionUID

  Serializable version identifier

  See Also:
    Constant Field Values

Constructor Detail

### AbstractIntegerDistribution

    protected AbstractIntegerDistribution()

  Default constructor.

Method Detail

### cumulativeProbability

    public double cumulativeProbability(double x)
                                 throws MathException

  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, or CDF, for this distribution.

  If `x` does not represent an integer value, the CDF is evaluated at the greatest integer less than x.

  Specified by:
    `cumulativeProbability` in interface `Distribution`
  Parameters:
    `x` - the value at which the distribution function is evaluated.
  Returns:
    cumulative probability that a random variable with this distribution takes a value less than or equal to `x`
  Throws:
    `MathException` - if the cumulative probability can not be computed due to convergence or other numerical errors.

### cumulativeProbability

    public double cumulativeProbability(double x0,
                                        double x1)
                                 throws MathException

  For a random variable X whose values are distributed according to this distribution, this method returns P(x0 ≤ X ≤ x1).

  Specified by:
    `cumulativeProbability` in interface `Distribution`
  Overrides:
    `cumulativeProbability` in class `AbstractDistribution`
  Parameters:
    `x0` - the (inclusive) lower bound
    `x1` - the (inclusive) upper bound
  Returns:
    the probability that a random variable with this distribution will take a value between `x0` and `x1`, including the endpoints.
  Throws:
    `MathException` - if the cumulative probability can not be computed due to convergence or other numerical errors.
    `java.lang.IllegalArgumentException` - if `x0 > x1`

### cumulativeProbability

    public abstract double cumulativeProbability(int x)
                                          throws MathException

  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 distribution function, or PDF, for this distribution.

  Specified by:
    `cumulativeProbability` in interface `IntegerDistribution`
  Parameters:
    `x` - the value at which the PDF is evaluated.
  Returns:
    PDF for this distribution.
  Throws:
    `MathException` - if the cumulative probability can not be computed due to convergence or other numerical errors.

### probability

    public double probability(double 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, or PMF, for the distribution.

  If `x` does not represent an integer value, 0 is returned.

  Specified by:
    `probability` in interface `DiscreteDistribution`
  Parameters:
    `x` - the value at which the probability density function is evaluated
  Returns:
    the value of the probability density function at x

### cumulativeProbability

    public double cumulativeProbability(int x0,
                                        int x1)
                                 throws MathException

  For a random variable X whose values are distributed according to this distribution, this method returns P(x0 ≤ X ≤ x1).

  Specified by:
    `cumulativeProbability` in interface `IntegerDistribution`
  Parameters:
    `x0` - the inclusive, lower bound
    `x1` - the inclusive, upper bound
  Returns:
    the cumulative probability.
  Throws:
    `MathException` - if the cumulative probability can not be computed due to convergence or other numerical errors.
    `java.lang.IllegalArgumentException` - if x0 > x1

### inverseCumulativeProbability

    public int inverseCumulativeProbability(double p)
                                     throws MathException

  For a random variable X whose values are distributed according to this distribution, this method returns the largest x, such that P(X ≤ x) ≤ `p`.

  Specified by:
    `inverseCumulativeProbability` in interface `IntegerDistribution`
  Parameters:
    `p` - the desired probability
  Returns:
    the largest x such that P(X ≤ x) <= p
  Throws:
    `MathException` - if the inverse cumulative probability can not be computed due to convergence or other numerical errors.
    `java.lang.IllegalArgumentException` - if p < 0 or p > 1

### checkedCumulativeProbability

    private double checkedCumulativeProbability(int argument)
                                         throws FunctionEvaluationException

  Computes the cumulative probablity function and checks for NaN values returned. Throws MathException if the value is NaN. Wraps and rethrows any MathException encountered evaluating the cumulative probability function in a FunctionEvaluationException. Throws FunctionEvaluationException of the cumulative probability function returns NaN.

  Parameters:
    `argument` - input value
  Returns:
    cumulative probability
  Throws:
    `FunctionEvaluationException` - if a MathException occurs computing the cumulative probability

### getDomainLowerBound

    protected abstract int getDomainLowerBound(double p)

  Access the domain value lower bound, based on `p`, used to bracket a PDF root. This method is used by `inverseCumulativeProbability(double)` to find critical values.

  Parameters:
    `p` - the desired probability for the critical value
  Returns:
    domain value lower bound, i.e. P(X < lower bound) < `p`

### getDomainUpperBound

    protected abstract int getDomainUpperBound(double p)

  Access the domain value upper bound, based on `p`, used to bracket a PDF root. This method is used by `inverseCumulativeProbability(double)` to find critical values.

  Parameters:
    `p` - the desired probability for the critical value
  Returns:
    domain value upper bound, i.e. P(X < upper bound) > `p`

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