org.apache.commons.math.distribution

## Interface IntegerDistribution

• ### Method Summary

All Methods
Modifier and Type Method and Description
`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 this distribution, X, this method returns P(x0 ≤ X ≤ x1).
`int` `inverseCumulativeProbability(double p)`
For this distribution, X, this method returns the largest x such that P(X ≤ x) <= p.
`double` `probability(int x)`
For a random variable X whose values are distributed according to this distribution, this method returns P(X = x).
• ### Methods inherited from interface org.apache.commons.math.distribution.DiscreteDistribution

`probability`
• ### Methods inherited from interface org.apache.commons.math.distribution.Distribution

`cumulativeProbability, cumulativeProbability`
• ### 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 for the distribution.
Parameters:
`x` - the value at which the probability density function is evaluated.
Returns:
the value of the probability density function at x
• #### cumulativeProbability

```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 the distribution.
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.
• #### cumulativeProbability

```double cumulativeProbability(int x0,
int x1)
throws MathException```
For this distribution, X, this method returns P(x0 ≤ X ≤ x1).
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

```int inverseCumulativeProbability(double p)
throws MathException```
For this distribution, X, this method returns the largest x such that P(X ≤ x) <= p.

Note that this definition implies:

• If there is a minimum value, `m`, with positive probability under (the density of) X, then `m - 1` is returned by `inverseCumulativeProbability(0).` If there is no such value `m, Integer.MIN_VALUE` is returned.
• If there is a maximum value, `M`, such that P(X ≤ M) =1, then `M` is returned by `inverseCumulativeProbability(1).` If there is no such value, `M, Integer.MAX_VALUE` is returned.

Parameters:
`p` - the cumulative 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 is not between 0 and 1 (inclusive)