org.apache.commons.math3.distribution

## Class TriangularDistribution

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

random, randomData, SOLVER_DEFAULT_ABSOLUTE_ACCURACY
• ### Constructor Summary

Constructors
Constructor and Description
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

Methods
Modifier and Type Method and Description
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, logDensity, 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.

Note: this constructor will implicitly create an instance of Well19937c as random generator to be used for sampling only (see AbstractRealDistribution.sample() and AbstractRealDistribution.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 - 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
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