Package org.apache.commons.math4.distribution

Class AbstractIntegerDistribution

java.lang.Object

org.apache.commons.math4.distribution.AbstractIntegerDistribution

All Implemented Interfaces:

java.io.Serializable, IntegerDistribution, DiscreteDistribution

Direct Known Subclasses:

EnumeratedIntegerDistribution

public abstract class AbstractIntegerDistribution
extends java.lang.Object
implements IntegerDistribution, java.io.Serializable

Base class for integer-valued discrete distributions. Default implementations are provided for some of the methods that do not vary from distribution to distribution.

See Also:

Serialized Form

Nested Class Summary

Nested classes/interfaces inherited from interface org.apache.commons.statistics.distribution.DiscreteDistribution

DiscreteDistribution.Sampler

Constructor Summary

Constructors

Constructor	Description
AbstractIntegerDistribution()

Method Summary

Modifier and Type	Method	Description
DiscreteDistribution.Sampler	createSampler(UniformRandomProvider rng)	Creates a sampler.
int	inverseCumulativeProbability(double p)	Computes the quantile function of this distribution.
double	logProbability(int x)	For a random variable X whose values are distributed according to this distribution, this method returns log(P(X = x)), where log is the natural logarithm.
double	probability(int x0, int x1)	For a random variable X whose values are distributed according to this distribution, this method returns P(x0 < X <= x1).
static int[]	sample(int n, DiscreteDistribution.Sampler sampler)	Utility function for allocating an array and filling it with n samples generated by the given sampler.
protected int	solveInverseCumulativeProbability(double p, int lower, int upper)	This is a utility function used by inverseCumulativeProbability(double).

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Methods inherited from interface org.apache.commons.statistics.distribution.DiscreteDistribution

cumulativeProbability, getMean, getSupportLowerBound, getSupportUpperBound, getVariance, isSupportConnected, probability

Constructor Detail

AbstractIntegerDistribution

public AbstractIntegerDistribution()

Method Detail

probability

public double probability(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). The default implementation uses the identity

P(x0 < X <= x1) = P(X <= x1) - P(X <= x0)

Specified by:

probability in interface DiscreteDistribution

Parameters:

x0 - Lower bound (exclusive).

x1 - Upper bound (inclusive).

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

Since:

4.0, was previously named cumulativeProbability

inverseCumulativeProbability

public 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. The default implementation returns

• DiscreteDistribution.getSupportLowerBound() for p = 0,
• DiscreteDistribution.getSupportUpperBound() for p = 1, and
• solveInverseCumulativeProbability(double, int, int) for 0 < p < 1.

Specified by:

inverseCumulativeProbability in interface DiscreteDistribution

Parameters:

p - Cumulative probability.

Returns:

the smallest p-quantile of this distribution (largest 0-quantile for p = 0).

Throws:

OutOfRangeException

solveInverseCumulativeProbability

protected int solveInverseCumulativeProbability(double p,
                                                int lower,
                                                int upper)

This is a utility function used by inverseCumulativeProbability(double). It assumes 0 < p < 1 and that the inverse cumulative probability lies in the bracket (lower, upper]. The implementation does simple bisection to find the smallest p-quantile inf{x in Z | P(X<=x) >= p}.

Parameters:

p - the cumulative probability

lower - a value satisfying cumulativeProbability(lower) < p

upper - a value satisfying p <= cumulativeProbability(upper)

Returns:

the smallest p-quantile of this distribution

logProbability

public double logProbability(int x)

For a random variable X whose values are distributed according to this distribution, this method returns log(P(X = x)), where log is the natural logarithm.

The default implementation simply computes the logarithm of probability(x).

Specified by:

logProbability in interface DiscreteDistribution

Parameters:

x - Point at which the PMF is evaluated.

Returns:

the logarithm of the value of the probability mass function at x.

sample

public static int[] sample(int n,
                           DiscreteDistribution.Sampler sampler)

Utility function for allocating an array and filling it with n samples generated by the given sampler.

Parameters:

n - Number of samples.

sampler - Sampler.

Returns:

an array of size n.

createSampler

public DiscreteDistribution.Sampler createSampler(UniformRandomProvider rng)

Creates a sampler.

Specified by:

createSampler in interface DiscreteDistribution

Parameters:

rng - Generator of uniformly distributed numbers.

Returns:

a sampler that produces random numbers according this distribution.