org.apache.commons.math3.distribution

Class AbstractRealDistribution

java.lang.Object

org.apache.commons.math3.distribution.AbstractRealDistribution

All Implemented Interfaces:

java.io.Serializable, RealDistribution

Direct Known Subclasses:

BetaDistribution, CauchyDistribution, ChiSquaredDistribution, ConstantRealDistribution, EmpiricalDistribution, EnumeratedRealDistribution, ExponentialDistribution, FDistribution, GammaDistribution, GumbelDistribution, LaplaceDistribution, LevyDistribution, LogisticDistribution, LogNormalDistribution, NakagamiDistribution, NormalDistribution, ParetoDistribution, TDistribution, TriangularDistribution, UniformRealDistribution, WeibullDistribution

public abstract class AbstractRealDistribution
extends java.lang.Object
implements RealDistribution, java.io.Serializable

Base class for probability distributions on the reals. Default implementations are provided for some of the methods that do not vary from distribution to distribution.

Since:

3.0

See Also:

Serialized Form

Field Summary

Fields

Modifier and Type	Field and Description
static double	SOLVER_DEFAULT_ABSOLUTE_ACCURACY Default accuracy.

Method Summary

Modifier and Type	Method and Description
double	cumulativeProbability(double x0, double x1) Deprecated. As of 3.1 (to be removed in 4.0). Please use probability(double,double) instead.
double	inverseCumulativeProbability(double p) Computes the quantile function of this distribution.
double	logDensity(double x) Returns the natural logarithm of the probability density function (PDF) of this distribution evaluated at the specified point x.
double	probability(double x) For a random variable X whose values are distributed according to this distribution, this method returns P(X = x).
double	probability(double x0, double x1) For a random variable X whose values are distributed according to this distribution, this method returns P(x0 < X <= x1).
void	reseedRandomGenerator(long seed) Reseed the random generator used to generate samples.
double	sample() Generate a random value sampled from this distribution.
double[]	sample(int sampleSize) Generate a random sample from the distribution.

Methods inherited from class java.lang.Object

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

Methods inherited from interface org.apache.commons.math3.distribution.RealDistribution

cumulativeProbability, density, getNumericalMean, getNumericalVariance, getSupportLowerBound, getSupportUpperBound, isSupportConnected, isSupportLowerBoundInclusive, isSupportUpperBoundInclusive

Field Detail

SOLVER_DEFAULT_ABSOLUTE_ACCURACY

public static final double SOLVER_DEFAULT_ABSOLUTE_ACCURACY

Default accuracy.

See Also:

Constant Field Values

Method Detail

cumulativeProbability

@Deprecated
public double cumulativeProbability(double x0,
                                                double x1)
                                         throws NumberIsTooLargeException

Deprecated. As of 3.1 (to be removed in 4.0). Please use probability(double,double) instead.

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 RealDistribution

Parameters:

x0 - the exclusive lower bound

x1 - the inclusive upper bound

Returns:

the probability that a random variable with this distribution takes a value between x0 and x1, excluding the lower and including the upper endpoint

Throws:

NumberIsTooLargeException - if x0 > x1

probability

public double probability(double x0,
                          double x1)

For a random variable X whose values are distributed according to this distribution, this method returns P(x0 < X <= x1).

Parameters:

x0 - Lower bound (excluded).

x1 - Upper bound (included).

Returns:

the probability that a random variable with this distribution takes a value between x0 and x1, excluding the lower and including the upper endpoint.

Throws:

NumberIsTooLargeException - if x0 > x1. The default implementation uses the identity P(x0 < X <= x1) = P(X <= x1) - P(X <= x0)

Since:

3.1

inverseCumulativeProbability

public double 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 R | P(X<=x) >= p} for 0 < p <= 1,
• inf{x in R | P(X<=x) > 0} for p = 0.

The default implementation returns

• RealDistribution.getSupportLowerBound() for p = 0,
• RealDistribution.getSupportUpperBound() for p = 1.

Specified by:

inverseCumulativeProbability in interface RealDistribution

Parameters:

p - the cumulative probability

Returns:

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

Throws:

OutOfRangeException - if p < 0 or p > 1

reseedRandomGenerator

public void reseedRandomGenerator(long seed)

Reseed the random generator used to generate samples.

Specified by:

reseedRandomGenerator in interface RealDistribution

Parameters:

seed - the new seed

sample

public double sample()

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

Specified by:

sample in interface RealDistribution

Returns:

a random value.

sample

public double[] 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 RealDistribution

Parameters:

sampleSize - the number of random values to generate

Returns:

an array representing the random sample

probability

public double probability(double 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 (PMF) for the distribution.

Specified by:

probability in interface RealDistribution

Parameters:

x - the point at which the PMF is evaluated

Returns:

zero.

Since:

3.1

logDensity

public double logDensity(double x)

Returns the natural logarithm of the probability density function (PDF) of this distribution evaluated at the specified point x. In general, the PDF is the derivative of the CDF. If the derivative does not exist at x, then an appropriate replacement should be returned, e.g. Double.POSITIVE_INFINITY, Double.NaN, or the limit inferior or limit superior of the difference quotient. 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 RealDistribution.density(double). The default implementation simply computes the logarithm of density(x).

Parameters:

x - the point at which the PDF is evaluated

Returns:

the logarithm of the value of the probability density function at point x