org.apache.commons.math3.distribution
Interface RealDistribution

All Known Implementing Classes:

AbstractRealDistribution, BetaDistribution, CauchyDistribution, ChiSquaredDistribution, EmpiricalDistribution, ExponentialDistribution, FDistribution, GammaDistribution, LogNormalDistribution, NormalDistribution, TDistribution, TriangularDistribution, UniformRealDistribution, WeibullDistribution

public interface RealDistribution

Base interface for distributions on the reals.

Since:

3.0

Version:

$Id: RealDistribution.java 7721 2013-02-14 14:07:13Z CardosoP $

Method Summary

double	cumulativeProbability(double x) For a random variable X whose values are distributed according to this distribution, this method returns P(X <= x).
double	cumulativeProbability(double x0, double x1) Deprecated. As of 3.1. In 4.0, this method will be renamed probability(double x0, double x1).
double	density(double x) Returns the probability density function (PDF) of this distribution evaluated at the specified point x.
double	getNumericalMean() Use this method to get the numerical value of the mean of this distribution.
double	getNumericalVariance() Use this method to get the numerical value of the variance of this distribution.
double	getSupportLowerBound() Access the lower bound of the support.
double	getSupportUpperBound() Access the upper bound of the support.
double	inverseCumulativeProbability(double p) Computes the quantile function of this distribution.
boolean	isSupportConnected() Use this method to get information about whether the support is connected, i.e.
boolean	isSupportLowerBoundInclusive() Deprecated. to be removed in 4.0
boolean	isSupportUpperBoundInclusive() Deprecated. to be removed in 4.0
double	probability(double x) For a random variable X whose values are distributed according to this distribution, this method returns P(X = x).
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.

Method Detail

probability

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.

Parameters:

x - the point at which the PMF is evaluated

Returns:

the value of the probability mass function at point x

density

double density(double x)

Returns 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.

Parameters:

x - the point at which the PDF is evaluated

Returns:

the value of the probability density function at point x

cumulativeProbability

double cumulativeProbability(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 (cumulative) distribution function (CDF) for this distribution.

Parameters:

x - the point at which the CDF is evaluated

Returns:

the probability that a random variable with this distribution takes a value less than or equal to x

cumulativeProbability

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

Deprecated. As of 3.1. In 4.0, this method will be renamed 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 - 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

inverseCumulativeProbability

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.

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

getNumericalMean

double getNumericalMean()

Use this method to get the numerical value of the mean of this distribution.

Returns:

the mean or Double.NaN if it is not defined

getNumericalVariance

double getNumericalVariance()

Use this method to get the numerical value of the variance of this distribution.

Returns:

the variance (possibly Double.POSITIVE_INFINITY as for certain cases in TDistribution) or Double.NaN if it is not defined

getSupportLowerBound

double getSupportLowerBound()

Access the lower bound of the support. This method must return the same value as inverseCumulativeProbability(0). In other words, this method must return

inf {x in R | P(X <= x) > 0}.

Returns:

lower bound of the support (might be Double.NEGATIVE_INFINITY)

getSupportUpperBound

double getSupportUpperBound()

Access the upper bound of the support. This method must return the same value as inverseCumulativeProbability(1). In other words, this method must return

inf {x in R | P(X <= x) = 1}.

Returns:

upper bound of the support (might be Double.POSITIVE_INFINITY)

isSupportLowerBoundInclusive

boolean isSupportLowerBoundInclusive()

Deprecated. to be removed in 4.0

Whether or not the lower bound of support is in the domain of the density function. Returns true iff getSupporLowerBound() is finite and density(getSupportLowerBound()) returns a non-NaN, non-infinite value.

Returns:

true if the lower bound of support is finite and the density function returns a non-NaN, non-infinite value there

isSupportUpperBoundInclusive

boolean isSupportUpperBoundInclusive()

Deprecated. to be removed in 4.0

Whether or not the upper bound of support is in the domain of the density function. Returns true iff getSupportUpperBound() is finite and density(getSupportUpperBound()) returns a non-NaN, non-infinite value.

Returns:

true if the upper bound of support is finite and the density function returns a non-NaN, non-infinite value there

isSupportConnected

boolean isSupportConnected()

Use this method to get information about whether the support is connected, i.e. whether all values between the lower and upper bound of the support are included in the support.

Returns:

whether the support is connected or not

reseedRandomGenerator

void reseedRandomGenerator(long seed)

Reseed the random generator used to generate samples.

Parameters:

seed - the new seed

sample

double sample()

Generate a random value sampled from this distribution.

Returns:

a random value.

sample

double[] sample(int sampleSize)

Generate a random sample from the distribution.

Parameters:

sampleSize - the number of random values to generate

Returns:

an array representing the random sample

Throws:

NotStrictlyPositiveException - if sampleSize is not positive