org.apache.commons.math3.distribution

## Interface IntegerDistribution

All Known Implementing Classes:
  AbstractIntegerDistribution, BinomialDistribution, HypergeometricDistribution, PascalDistribution, PoissonDistribution, UniformIntegerDistribution, ZipfDistribution

    public interface IntegerDistribution

Interface for distributions on the integers.

Version:
  $Id: IntegerDistribution.java 1416643 2012-12-03 19:37:14Z tn $

### Method Summary

Methods
`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)`.
`double` `getNumericalMean()` Use this method to get the numerical value of the mean of this distribution.
`double` `getNumericalVariance()` Use this method to get the numerical value of the variance of this distribution.
`int` `getSupportLowerBound()` Access the lower bound of the support.
`int` `getSupportUpperBound()` Access the upper bound of the support.
`int` `inverseCumulativeProbability(double p)` Computes the quantile function of this distribution.
`boolean` `isSupportConnected()` Use this method to get information about whether the support is connected, i.e.
`double` `probability(int x)` For a random variable `X` whose values are distributed according to this distribution, this method returns `P(X = x)`.
`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.

### Method Detail

#### probability

    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` - the point at which the PMF is evaluated
Returns:
  the value of the probability mass function at `x`

#### cumulativeProbability

    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` - the 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`

#### cumulativeProbability

    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)`.

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

    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.

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`

#### getNumericalMean

    double getNumericalMean()

Use this method to get the numerical value of the mean of this distribution.

Returns:
  the mean or `Double.NaN` if it is not defined

#### getNumericalVariance

    double getNumericalVariance()

Use this method to get the numerical value of the variance of this distribution.

Returns:
  the variance (possibly `Double.POSITIVE_INFINITY` or `Double.NaN` if it is not defined)

#### getSupportLowerBound

    int getSupportLowerBound()

Access the lower bound of the support. This method must return the same value as `inverseCumulativeProbability(0)`. In other words, this method must return

`inf {x in Z | P(X <= x) > 0}`.

Returns:
  lower bound of the support (`Integer.MIN_VALUE` for negative infinity)

#### getSupportUpperBound

    int getSupportUpperBound()

Access the upper bound of the support. This method must return the same value as `inverseCumulativeProbability(1)`. In other words, this method must return

`inf {x in R | P(X <= x) = 1}`.

Returns:
  upper bound of the support (`Integer.MAX_VALUE` for positive infinity)

#### isSupportConnected

    boolean isSupportConnected()

Use this method to get information about whether the support is connected, i.e. whether all integers between the lower and upper bound of the support are included in the support.

Returns:
  whether the support is connected or not

#### reseedRandomGenerator

    void reseedRandomGenerator(long seed)

Reseed the random generator used to generate samples.

Parameters:
  `seed` - the new seed
Since:
  3.0

#### sample

    int sample()

Generate a random value sampled from this distribution.

Returns:
  a random value
Since:
  3.0

#### sample

    int[] sample(int sampleSize)

Generate a random sample from the distribution.

Parameters:
  `sampleSize` - the number of random values to generate
Returns:
  an array representing the random sample
Throws:
  `NotStrictlyPositiveException` - if `sampleSize` is not positive
Since:
  3.0