fr.cnes.sirius.patrius.math.distribution

Class AbstractIntegerDistribution

java.lang.Object

fr.cnes.sirius.patrius.math.distribution.AbstractIntegerDistribution

All Implemented Interfaces:

IntegerDistribution, Serializable

Direct Known Subclasses:

BinomialDistribution, 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.

Version:

$Id: AbstractIntegerDistribution.java 18108 2017-10-04 06:45:27Z bignon $

See Also:

Serialized Form

Field Summary

Fields

Modifier and Type	Field and Description
protected RandomGenerator	random RNG instance used to generate samples from the distribution.

Constructor Summary

Constructors

Modifier	Constructor and Description
protected	AbstractIntegerDistribution(RandomGenerator rng)

Method Summary

Methods

Modifier and Type	Method and Description
double	cumulativeProbability(int x0, int x1) For a random variable X whose values are distributed according to this distribution, this method returns P(x0 < X <= x1).
int	inverseCumulativeProbability(double p) Computes the quantile function of this distribution.
void	reseedRandomGenerator(long seed) Reseed the random generator used to generate samples.
int	sample() Generate a random value sampled from this distribution.
int[]	sample(int sampleSize) Generate a random sample from the distribution.
protected int	solveInverseCumulativeProbability(double p, int lowerIn, int upperIn) 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 fr.cnes.sirius.patrius.math.distribution.IntegerDistribution

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

Field Detail

random

protected final RandomGenerator random

RNG instance used to generate samples from the distribution.

Since:

3.1

Constructor Detail

AbstractIntegerDistribution

protected AbstractIntegerDistribution(RandomGenerator rng)

Parameters:

rng - Random number generator.

Since:

3.1

Method Detail

cumulativeProbability

public double cumulativeProbability(int x0,
                           int x1)

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:

cumulativeProbability 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

inverseCumulativeProbability

public int inverseCumulativeProbability(double p)

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)

solveInverseCumulativeProbability

protected int solveInverseCumulativeProbability(double p,
                                    int lowerIn,
                                    int upperIn)

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

lowerIn - a value satisfying cumulativeProbability(lower) < p

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

Returns:

the smallest p-quantile of this distribution

reseedRandomGenerator

public void reseedRandomGenerator(long seed)

Reseed the random generator used to generate samples.

Specified by:

reseedRandomGenerator in interface IntegerDistribution

Parameters:

seed - the new seed

sample

public int sample()

Generate a random value sampled from this distribution. The default implementation uses the inversion method.

Specified by:

sample in interface IntegerDistribution

Returns:

a random value

sample

public int[] sample(int sampleSize)

Generate a random sample from the distribution. The default implementation generates the sample by calling sample() in a loop.

Specified by:

sample in interface IntegerDistribution

Parameters:

sampleSize - the number of random values to generate

Returns:

an array representing the random sample