org.apache.commons.math3.distribution
Class TriangularDistribution

java.lang.Object
  extended by org.apache.commons.math3.distribution.AbstractRealDistribution
      extended by 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 1292741 2012-02-23 11:26:36Z erans $
See Also:
Triangular distribution (Wikipedia), Serialized Form

Field Summary
private  double a
          Lower limit of this distribution (inclusive).
private  double b
          Upper limit of this distribution (inclusive).
private  double c
          Mode of this distribution.
private static long serialVersionUID
          Serializable version identifier.
private  double solverAbsoluteAccuracy
          Inverse cumulative probability accuracy.
 
Fields inherited from class org.apache.commons.math3.distribution.AbstractRealDistribution
randomData, SOLVER_DEFAULT_ABSOLUTE_ACCURACY
 
Constructor Summary
TriangularDistribution(double a, double c, double b)
          Create a triangular real distribution using the given lower limit, upper limit, and mode.
 
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()
          Use this method to get information about whether the lower bound of the support is inclusive or not.
 boolean isSupportUpperBoundInclusive()
          Use this method to get information about whether the upper bound of the support is inclusive or not.
 double probability(double x)
          For a random variable X whose values are distributed according to this distribution, this method returns P(X = x).
 
Methods inherited from class org.apache.commons.math3.distribution.AbstractRealDistribution
cumulativeProbability, reseedRandomGenerator, sample, sample
 
Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
 

Field Detail

serialVersionUID

private static final long serialVersionUID
Serializable version identifier.

See Also:
Constant Field Values

a

private final double a
Lower limit of this distribution (inclusive).


b

private final double b
Upper limit of this distribution (inclusive).


c

private final double c
Mode of this distribution.


solverAbsoluteAccuracy

private final double solverAbsoluteAccuracy
Inverse cumulative probability accuracy.

Constructor Detail

TriangularDistribution

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

probability

public 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. For this distribution P(X = x) always evaluates to 0.

Parameters:
x - the point at which the PMF is evaluated
Returns:
0

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

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

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()
Use this method to get information about whether the lower bound of the support is inclusive or not.

Returns:
whether the lower bound of the support is inclusive or not

isSupportUpperBoundInclusive

public boolean isSupportUpperBoundInclusive()
Use this method to get information about whether the upper bound of the support is inclusive or not.

Returns:
whether the upper bound of the support is inclusive or not

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 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


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