org.apache.commons.math.distribution
Interface IntegerDistribution

All Superinterfaces:

DiscreteDistribution, Distribution

All Known Subinterfaces:

BinomialDistribution, HypergeometricDistribution, PoissonDistribution

All Known Implementing Classes:

AbstractIntegerDistribution, BinomialDistributionImpl, HypergeometricDistributionImpl, PoissonDistributionImpl

public interface IntegerDistribution

extends DiscreteDistribution

Interface for discrete distributions of integer-valued random variables.

Version:

$Revision: 1.2 $ $Date: 2004/11/07 20:39:15 $

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 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

public 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

public 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

public 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.

IllegalArgumentException - if x0 > x1

inverseCumulativeProbability

public 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 postive probablility 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.

IllegalArgumentException - if p is not between 0 and 1 (inclusive)