org.apache.commons.math3.distribution
Class TriangularDistribution

java.lang.Object
  org.apache.commons.math3.distribution.AbstractRealDistribution
      org.apache.commons.math3.distribution.TriangularDistribution

All Implemented Interfaces:

Serializable, RealDistribution

public class TriangularDistribution
extends AbstractRealDistribution

Implementation of the triangular real distribution.

Since:

3.0

Version:

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

See Also:

Triangular distribution (Wikipedia), Serialized Form

Field Summary

Fields inherited from class org.apache.commons.math3.distribution.AbstractRealDistribution

random, randomData, SOLVER_DEFAULT_ABSOLUTE_ACCURACY

Constructor Summary

TriangularDistribution(double a, double c, double b)
Creates a triangular real distribution using the given lower limit, upper limit, and mode.

TriangularDistribution(RandomGenerator rng, double a, double c, double b)
Creates a triangular distribution.

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	density(double x) Returns the probability density function (PDF) of this distribution evaluated at the specified point x.
double	getMode() Returns the mode c of this distribution.
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.
protected double	getSolverAbsoluteAccuracy() Returns the solver absolute accuracy for inverse cumulative computation.
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() Whether or not the lower bound of support is in the domain of the density function.
boolean	isSupportUpperBoundInclusive() Whether or not the upper bound of support is in the domain of the density function.

Methods inherited from class org.apache.commons.math3.distribution.AbstractRealDistribution

cumulativeProbability, probability, probability, reseedRandomGenerator, sample, sample

Methods inherited from class java.lang.Object

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

Constructor Detail

TriangularDistribution

public TriangularDistribution(double a,
                              double c,
                              double b)
                       throws NumberIsTooLargeException,
                              NumberIsTooSmallException

Creates a triangular real distribution using the given lower limit, upper limit, and mode.

Parameters:

a - Lower limit of this distribution (inclusive).

b - Upper limit of this distribution (inclusive).

c - Mode of this distribution.

Throws:

NumberIsTooLargeException - if a >= b or if c > b.

NumberIsTooSmallException - if c < a.

TriangularDistribution

public TriangularDistribution(RandomGenerator rng,
                              double a,
                              double c,
                              double b)
                       throws NumberIsTooLargeException,
                              NumberIsTooSmallException

Creates a triangular distribution.

Parameters:

rng - Random number generator.

a - Lower limit of this distribution (inclusive).

b - Upper limit of this distribution (inclusive).

c - Mode of this distribution.

Throws:

NumberIsTooLargeException - if a >= b or if c > b.

NumberIsTooSmallException - if c < a.

Since:

3.1

Method Detail

getMode

public double getMode()

Returns the mode c of this distribution.

Returns:

the mode c of this distribution

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.

For this distribution, the returned value is not really meaningful, since exact formulas are implemented for the computation of the inverseCumulativeProbability(double) (no solver is invoked).

For lower limit a and upper limit b, the current implementation returns max(ulp(a), ulp(b).

Overrides:

getSolverAbsoluteAccuracy in class AbstractRealDistribution

Returns:

the maximum absolute error in inverse cumulative probability estimates

density

public 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. For lower limit a, upper limit b and mode c, the PDF is given by

• 2 * (x - a) / [(b - a) * (c - a)] if a <= x < c,
• 2 / (b - a) if x = c,
• 2 * (b - x) / [(b - a) * (b - c)] if c < x <= b,
• 0 otherwise.

Parameters:

x - the point at which the PDF is evaluated

Returns:

the value of the probability density function at point x

cumulativeProbability

public 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. For lower limit a, upper limit b and mode c, the CDF is given by

• 0 if x < a,
• (x - a)^2 / [(b - a) * (c - a)] if a <= x < c,
• (c - a) / (b - a) if x = c,
• 1 - (b - x)^2 / [(b - a) * (b - c)] if c < x <= b,
• 1 if x > b.

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

getNumericalMean

public double getNumericalMean()

Use this method to get the numerical value of the mean of this distribution. For lower limit a, upper limit b, and mode c, the mean is (a + b + c) / 3.

Returns:

the mean or Double.NaN if it is not defined

getNumericalVariance

public double getNumericalVariance()

Use this method to get the numerical value of the variance of this distribution. For lower limit a, upper limit b, and mode c, the variance is (a^2 + b^2 + c^2 - a * b - a * c - b * c) / 18.

Returns:

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

getSupportLowerBound

public 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}.

The lower bound of the support is equal to the lower limit parameter a of the distribution.

Returns:

lower bound of the support

getSupportUpperBound

public 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}.

The upper bound of the support is equal to the upper limit parameter b of the distribution.

Returns:

upper bound of the support

isSupportLowerBoundInclusive

public boolean isSupportLowerBoundInclusive()

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

public boolean isSupportUpperBoundInclusive()

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

public 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. The support of this distribution is connected.

Returns:

true

inverseCumulativeProbability

public double inverseCumulativeProbability(double p)
                                    throws OutOfRangeException

Description copied from class: AbstractRealDistribution

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

Overrides:

inverseCumulativeProbability in class AbstractRealDistribution

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