org.hipparchus.distribution.continuous

Class AbstractRealDistribution

java.lang.Object

org.hipparchus.distribution.continuous.AbstractRealDistribution

All Implemented Interfaces:

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 Object
implements RealDistribution, 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.

See Also:

Serialized Form

Field Summary

Fields

Modifier and Type	Field and Description
protected static double	DEFAULT_SOLVER_ABSOLUTE_ACCURACY Default absolute accuracy for inverse cumulative computation.

Constructor Summary

Constructors

Modifier	Constructor and Description
protected	AbstractRealDistribution() Create a real distribution with default solver absolute accuracy.
protected	AbstractRealDistribution(double solverAbsoluteAccuracy)

Method Summary

Modifier and Type	Method and Description
protected double	getSolverAbsoluteAccuracy() Returns the solver absolute accuracy for inverse cumulative computation.
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 x0, double x1) For a random variable X whose values are distributed according to this distribution, this method returns P(x0 < X <= x1).

Methods inherited from class java.lang.Object

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

Methods inherited from interface org.hipparchus.distribution.RealDistribution

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

Field Detail

DEFAULT_SOLVER_ABSOLUTE_ACCURACY

protected static final double DEFAULT_SOLVER_ABSOLUTE_ACCURACY

Default absolute accuracy for inverse cumulative computation.

See Also:

Constant Field Values

Constructor Detail

AbstractRealDistribution

protected AbstractRealDistribution(double solverAbsoluteAccuracy)

Parameters:

solverAbsoluteAccuracy - the absolute accuracy to use when computing the inverse cumulative probability.

AbstractRealDistribution

protected AbstractRealDistribution()

Create a real distribution with default solver absolute accuracy.

Method Detail

probability

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

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

Specified by:

probability in interface RealDistribution

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:

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

inverseCumulativeProbability

public double 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 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:

MathIllegalArgumentException - if p < 0 or p > 1

getSolverAbsoluteAccuracy

protected double getSolverAbsoluteAccuracy()

Returns the solver absolute accuracy for inverse cumulative computation. You can override this method in order to use a Brent solver with an absolute accuracy different from the default.

Returns:

the maximum absolute error in inverse cumulative probability estimates

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).

Specified by:

logDensity in interface RealDistribution

Parameters:

x - the point at which the PDF is evaluated

Returns:

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