Top Description Fields Constructors Methods
org.apache.commons.math3.distribution

public Class TriangularDistribution

extends AbstractRealDistribution
Class Inheritance
Imports
org.apache.commons.math3.exception.NumberIsTooLargeException, .NumberIsTooSmallException, .OutOfRangeException, org.apache.commons.math3.exception.util.LocalizedFormats, org.apache.commons.math3.random.RandomGenerator, .Well19937c, org.apache.commons.math3.util.FastMath
Implementation of the triangular real distribution.
Since
3.0
See Also
Triangular distribution (Wikipedia)

Field Summary

Modifier and TypeField and Description
private final double
a

Lower limit of this distribution (inclusive).

private final double
b

Upper limit of this distribution (inclusive).

private final double
c

Mode of this distribution.

private static final long
serialVersionUID

Hides org.apache.commons.math3.distribution.AbstractRealDistribution.serialVersionUID.

Serializable version identifier.
private final double
solverAbsoluteAccuracy

Hides org.apache.commons.math3.distribution.AbstractRealDistribution.solverAbsoluteAccuracy.

Inverse cumulative probability accuracy.
Inherited from org.apache.commons.math3.distribution.AbstractRealDistribution:
randomrandomDataSOLVER_DEFAULT_ABSOLUTE_ACCURACY

Constructor Summary

AccessConstructor and Description
public
TriangularDistribution(double
Lower limit of this distribution (inclusive).
a, double
Mode of this distribution.
c, double
Upper limit of this distribution (inclusive).
b)

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

public
TriangularDistribution(RandomGenerator
Random number generator.
rng, double
Lower limit of this distribution (inclusive).
a, double
Mode of this distribution.
c, double
Upper limit of this distribution (inclusive).
b)

Creates a triangular distribution.

Method Summary

Modifier and TypeMethod and Description
public double
cumulativeProbability(double
the point at which the CDF is evaluated
x)

Implements org.apache.commons.math3.distribution.RealDistribution.cumulativeProbability.

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

public double
density(double
the point at which the PDF is evaluated
x)

Implements org.apache.commons.math3.distribution.RealDistribution.density.

Returns the probability density function (PDF) of this distribution evaluated at the specified point x.

public double

Returns:

the mode c of this distribution
getMode()

Returns the mode c of this distribution.

public double
getNumericalMean()

Implements org.apache.commons.math3.distribution.RealDistribution.getNumericalMean.

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

public double
getNumericalVariance()

Implements org.apache.commons.math3.distribution.RealDistribution.getNumericalVariance.

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

protected double
getSolverAbsoluteAccuracy()

Overrides org.apache.commons.math3.distribution.AbstractRealDistribution.getSolverAbsoluteAccuracy.

Returns the solver absolute accuracy for inverse cumulative computation.

public double

Returns:

lower bound of the support
getSupportLowerBound()

Implements org.apache.commons.math3.distribution.RealDistribution.getSupportLowerBound.

Access the lower bound of the support.

public double

Returns:

upper bound of the support
getSupportUpperBound()

Implements org.apache.commons.math3.distribution.RealDistribution.getSupportUpperBound.

Access the upper bound of the support.

public double
inverseCumulativeProbability(double
the cumulative probability
p)

Overrides org.apache.commons.math3.distribution.AbstractRealDistribution.inverseCumulativeProbability.

Implements org.apache.commons.math3.distribution.RealDistribution.inverseCumulativeProbability.

Computes the quantile function of this distribution.

public boolean

Returns:

true
isSupportConnected()

Implements org.apache.commons.math3.distribution.RealDistribution.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.

public boolean
isSupportLowerBoundInclusive()

Implements org.apache.commons.math3.distribution.RealDistribution.isSupportLowerBoundInclusive.

Whether or not the lower bound of support is in the domain of the density function.

public boolean
isSupportUpperBoundInclusive()

Implements org.apache.commons.math3.distribution.RealDistribution.isSupportUpperBoundInclusive.

Whether or not the upper bound of support is in the domain of the density function.

Inherited from org.apache.commons.math3.distribution.AbstractRealDistribution:
cumulativeProbabilitylogDensityprobabilityprobabilityreseedRandomGeneratorsamplesample

Field Detail

aback to summary
private final double a

Lower limit of this distribution (inclusive).

bback to summary
private final double b

Upper limit of this distribution (inclusive).

cback to summary
private final double c

Mode of this distribution.

serialVersionUIDback to summary
private static final long serialVersionUID

Hides org.apache.commons.math3.distribution.AbstractRealDistribution.serialVersionUID.

Serializable version identifier.

solverAbsoluteAccuracyback to summary
private final double solverAbsoluteAccuracy

Hides org.apache.commons.math3.distribution.AbstractRealDistribution.solverAbsoluteAccuracy.

Inverse cumulative probability accuracy.

Constructor Detail

TriangularDistributionback to summary
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.

Note

this constructor will implicitly create an instance of Well19937c as random generator to be used for sampling only (see sample() and sample(int)). In case no sampling is needed for the created distribution, it is advised to pass null as random generator via the appropriate constructors to avoid the additional initialisation overhead.

Parameters
a:double

Lower limit of this distribution (inclusive).

c:double

Mode of this distribution.

b:double

Upper limit of this distribution (inclusive).

Exceptions
NumberIsTooLargeException:
if a >= b or if c > b.
NumberIsTooSmallException:
if c < a.
TriangularDistributionback to summary
public TriangularDistribution(RandomGenerator rng, double a, double c, double b) throws NumberIsTooLargeException, NumberIsTooSmallException

Creates a triangular distribution.

Parameters
rng:RandomGenerator

Random number generator.

a:double

Lower limit of this distribution (inclusive).

c:double

Mode of this distribution.

b:double

Upper limit of this distribution (inclusive).

Exceptions
NumberIsTooLargeException:
if a >= b or if c > b.
NumberIsTooSmallException:
if c < a.
Since
3.1

Method Detail

cumulativeProbabilityback to summary
public double cumulativeProbability(double x)

Implements org.apache.commons.math3.distribution.RealDistribution.cumulativeProbability.

Doc from org.apache.commons.math3.distribution.RealDistribution.cumulativeProbability.

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:double

the point at which the CDF is evaluated

Returns:double

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

densityback to summary
public double density(double x)

Implements org.apache.commons.math3.distribution.RealDistribution.density.

Doc from org.apache.commons.math3.distribution.RealDistribution.density.

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:double

the point at which the PDF is evaluated

Returns:double

the value of the probability density function at point x

getModeback to summary
public double getMode()

Returns the mode c of this distribution.

Returns:double

the mode c of this distribution

getNumericalMeanback to summary
public double getNumericalMean()

Implements org.apache.commons.math3.distribution.RealDistribution.getNumericalMean.

Doc from org.apache.commons.math3.distribution.RealDistribution.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:double

the mean or Double.NaN if it is not defined

getNumericalVarianceback to summary
public double getNumericalVariance()

Implements org.apache.commons.math3.distribution.RealDistribution.getNumericalVariance.

Doc from org.apache.commons.math3.distribution.RealDistribution.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:double

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

getSolverAbsoluteAccuracyback to summary
protected double getSolverAbsoluteAccuracy()

Overrides org.apache.commons.math3.distribution.AbstractRealDistribution.getSolverAbsoluteAccuracy.

Doc from org.apache.commons.math3.distribution.AbstractRealDistribution.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).

Returns:double

the maximum absolute error in inverse cumulative probability estimates

Annotations
@Override
getSupportLowerBoundback to summary
public double getSupportLowerBound()

Implements org.apache.commons.math3.distribution.RealDistribution.getSupportLowerBound.

Doc from org.apache.commons.math3.distribution.RealDistribution.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:double

lower bound of the support

getSupportUpperBoundback to summary
public double getSupportUpperBound()

Implements org.apache.commons.math3.distribution.RealDistribution.getSupportUpperBound.

Doc from org.apache.commons.math3.distribution.RealDistribution.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:double

upper bound of the support

inverseCumulativeProbabilityback to summary
public double inverseCumulativeProbability(double p) throws OutOfRangeException

Overrides org.apache.commons.math3.distribution.AbstractRealDistribution.inverseCumulativeProbability.

Implements org.apache.commons.math3.distribution.RealDistribution.inverseCumulativeProbability.

Doc from org.apache.commons.math3.distribution.AbstractRealDistribution.inverseCumulativeProbability.

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
Parameters
p:double

Doc from org.apache.commons.math3.distribution.RealDistribution.inverseCumulativeProbability.

the cumulative probability

Returns:double

Doc from org.apache.commons.math3.distribution.RealDistribution.inverseCumulativeProbability.

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

Annotations
@Override
Exceptions
OutOfRangeException:

Doc from org.apache.commons.math3.distribution.RealDistribution.inverseCumulativeProbability.

if p < 0 or p > 1

isSupportConnectedback to summary
public boolean isSupportConnected()

Implements org.apache.commons.math3.distribution.RealDistribution.isSupportConnected.

Doc from org.apache.commons.math3.distribution.RealDistribution.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:boolean

true

isSupportLowerBoundInclusiveback to summary
public boolean isSupportLowerBoundInclusive()

Implements org.apache.commons.math3.distribution.RealDistribution.isSupportLowerBoundInclusive.

Doc from org.apache.commons.math3.distribution.RealDistribution.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:boolean

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

isSupportUpperBoundInclusiveback to summary
public boolean isSupportUpperBoundInclusive()

Implements org.apache.commons.math3.distribution.RealDistribution.isSupportUpperBoundInclusive.

Doc from org.apache.commons.math3.distribution.RealDistribution.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:boolean

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