Package org.apache.commons.math.distribution

Interface IntegerDistribution

All Superinterfaces:

DiscreteDistribution, Distribution

All Known Subinterfaces:

BinomialDistribution, HypergeometricDistribution, PascalDistribution, PoissonDistribution, ZipfDistribution

All Known Implementing Classes:

AbstractIntegerDistribution, BinomialDistributionImpl, HypergeometricDistributionImpl, PascalDistributionImpl, PoissonDistributionImpl, ZipfDistributionImpl

public interface IntegerDistribution
extends DiscreteDistribution

Interface for discrete distributions of integer-valued random variables.

Method Summary

Modifier and Type	Method	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)