Package org.hipparchus.distribution.discrete

Class AbstractIntegerDistribution

java.lang.Object

org.hipparchus.distribution.discrete.AbstractIntegerDistribution

All Implemented Interfaces:

Serializable, IntegerDistribution

Direct Known Subclasses:

BinomialDistribution, EnumeratedIntegerDistribution, GeometricDistribution, HypergeometricDistribution, PascalDistribution, PoissonDistribution, UniformIntegerDistribution, ZipfDistribution

public abstract class AbstractIntegerDistribution
extends Object
implements IntegerDistribution, 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

Constructor Summary

Constructors

Constructor	Description
AbstractIntegerDistribution()

Method Summary

Modifier and Type	Method	Description
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).
protected int	solveInverseCumulativeProbability(double p, int lower, int upper)	This is a utility function used by inverseCumulativeProbability(double).

Methods inherited from interface org.hipparchus.distribution.IntegerDistribution

cumulativeProbability, getNumericalMean, getNumericalVariance, getSupportLowerBound, getSupportUpperBound, isSupportConnected, probability

Methods inherited from class java.lang.Object

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

Constructor Detail

AbstractIntegerDistribution

public AbstractIntegerDistribution()

Method Detail

probability

public double probability(int x0,
                          int x1)
                   throws MathIllegalArgumentException

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 IntegerDistribution

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:

MathIllegalArgumentException - if x0 > x1

inverseCumulativeProbability

public int inverseCumulativeProbability(double p)
                                 throws MathIllegalArgumentException

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

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

Specified by:

inverseCumulativeProbability in interface IntegerDistribution

Parameters:

p - the cumulative probability

Returns:

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

Throws:

MathIllegalArgumentException - if p < 0 or p > 1

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. In other words, this method represents the logarithm of the probability mass function (PMF) for the distribution. Note that due to the floating point precision and under/overflow issues, this method will for some distributions be more precise and faster than computing the logarithm of IntegerDistribution.probability(int).

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

Specified by:

logProbability in interface IntegerDistribution

Parameters:

x - the point at which the PMF is evaluated

Returns:

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