## 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
` 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