org.apache.commons.math3.distribution

## Class AbstractIntegerDistribution

- java.lang.Object
- - org.apache.commons.math3.distribution.AbstractIntegerDistribution

All Implemented Interfaces:
  Serializable, IntegerDistribution

Direct Known Subclasses:
  BinomialDistribution, HypergeometricDistribution, PascalDistribution, PoissonDistribution, UniformIntegerDistribution, ZipfDistribution

    public abstract class AbstractIntegerDistribution
    extends Object
    implements IntegerDistribution, 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:
  $Id: AbstractIntegerDistribution.java 1422195 2012-12-15 06:45:18Z psteitz $
See Also:
  Serialized Form

### Field Summary

Fields
`protected RandomGenerator` `random` RNG instance used to generate samples from the distribution.
`protected RandomDataImpl` `randomData` Deprecated. As of 3.1, to be removed in 4.0. Please use the `random` instance variable instead.
`private static long` `serialVersionUID` Serializable version identifier

### Constructor Summary

Constructors
`protected` `AbstractIntegerDistribution()` Deprecated. As of 3.1, to be removed in 4.0. Please use `AbstractIntegerDistribution(RandomGenerator)` instead.
`protected` `AbstractIntegerDistribution(RandomGenerator rng)`

### Method Summary

Methods
`private double` `checkedCumulativeProbability(int argument)` Computes the cumulative probability function and checks for `NaN` values returned.
`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)`.
`int` `inverseCumulativeProbability(double p)` Computes the quantile function of this distribution.
`void` `reseedRandomGenerator(long seed)` Reseed the random generator used to generate samples.
`int` `sample()` Generate a random value sampled from this distribution.
`int[]` `sample(int sampleSize)` Generate a random sample from the distribution.
`protected int` `solveInverseCumulativeProbability(double p, int lower, int upper)` This is a utility function used by `inverseCumulativeProbability(double)`.

### 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.math3.distribution.IntegerDistribution

`cumulativeProbability, getNumericalMean, getNumericalVariance, getSupportLowerBound, getSupportUpperBound, isSupportConnected, probability`

### Field Detail

#### serialVersionUID

    private static final long serialVersionUID

Serializable version identifier

See Also:
  Constant Field Values

#### randomData

    @Deprecated
    protected final RandomDataImpl randomData

Deprecated. As of 3.1, to be removed in 4.0. Please use the `random` instance variable instead.
RandomData instance used to generate samples from the distribution.

#### random

    protected final RandomGenerator random

RNG instance used to generate samples from the distribution.

Since:
  3.1

### Constructor Detail

#### AbstractIntegerDistribution

    @Deprecated
    protected AbstractIntegerDistribution()

Deprecated. As of 3.1, to be removed in 4.0. Please use `AbstractIntegerDistribution(RandomGenerator)` instead.

#### AbstractIntegerDistribution

    protected AbstractIntegerDistribution(RandomGenerator rng)

Parameters:
  `rng` - Random number generator.
Since:
  3.1

### Method Detail

#### cumulativeProbability

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

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)`

Specified by:
  `cumulativeProbability` in interface `IntegerDistribution`
Parameters:
  `x0` - the exclusive 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`, excluding the lower and including the upper endpoint
Throws:
  `NumberIsTooLargeException` - if `x0 > x1`

#### inverseCumulativeProbability

    public int inverseCumulativeProbability(double p)
                                     throws OutOfRangeException

Computes the quantile function of this distribution. For a random variable `X` distributed according to this distribution, the returned value is

- `inf{x in Z | P(X<=x) >= p}` for `0 < p <= 1`,
- `inf{x in Z | P(X<=x) > 0}` for `p = 0`.

If the result exceeds the range of the data type `int`, then `Integer.MIN_VALUE` or `Integer.MAX_VALUE` is returned. The default implementation returns

- `IntegerDistribution.getSupportLowerBound()` for `p = 0`,
- `IntegerDistribution.getSupportUpperBound()` for `p = 1`, and
- `solveInverseCumulativeProbability(double, int, int)` for `0 < p < 1`.

Specified by:
  `inverseCumulativeProbability` in interface `IntegerDistribution`
Parameters:
  `p` - the cumulative probability
Returns:
  the smallest `p`-quantile of this distribution (largest 0-quantile for `p = 0`)
Throws:
  `OutOfRangeException` - if `p < 0` or `p > 1`

#### solveInverseCumulativeProbability

    protected int solveInverseCumulativeProbability(double p,
                                        int lower,
                                        int upper)

This is a utility function used by `inverseCumulativeProbability(double)`. It assumes `0 < p < 1` and that the inverse cumulative probability lies in the bracket `(lower, upper]`. The implementation does simple bisection to find the smallest `p`-quantile `inf{x in Z | P(X<=x) >= p}`.

Parameters:
  `p` - the cumulative probability
  `lower` - a value satisfying `cumulativeProbability(lower) < p`
  `upper` - a value satisfying `p <= cumulativeProbability(upper)`
Returns:
  the smallest `p`-quantile of this distribution

#### reseedRandomGenerator

    public void reseedRandomGenerator(long seed)

Reseed the random generator used to generate samples.

Specified by:
  `reseedRandomGenerator` in interface `IntegerDistribution`
Parameters:
  `seed` - the new seed

#### sample

    public int sample()

Generate a random value sampled from this distribution. The default implementation uses the inversion method.

Specified by:
  `sample` in interface `IntegerDistribution`
Returns:
  a random value

#### sample

    public int[] sample(int sampleSize)

Generate a random sample from the distribution. The default implementation generates the sample by calling `sample()` in a loop.

Specified by:
  `sample` in interface `IntegerDistribution`
Parameters:
  `sampleSize` - the number of random values to generate
Returns:
  an array representing the random sample

#### checkedCumulativeProbability

    private double checkedCumulativeProbability(int argument)
                                         throws MathInternalError

Computes the cumulative probability function and checks for `NaN` values returned. Throws `MathInternalError` if the value is `NaN`. Rethrows any exception encountered evaluating the cumulative probability function. Throws `MathInternalError` if the cumulative probability function returns `NaN`.

Parameters:
  `argument` - input value
Returns:
  the cumulative probability
Throws:
  `MathInternalError` - if the cumulative probability is `NaN`