TriangularDistribution (patrimoine de base SIRIUS 4.16 API)

java.lang.Object
- fr.cnes.sirius.patrius.math.distribution.AbstractRealDistribution
- - fr.cnes.sirius.patrius.math.distribution.TriangularDistribution

All Implemented Interfaces:

RealDistribution, Serializable
```
public class TriangularDistribution
extends AbstractRealDistribution
```
Implementation of the triangular real distribution.

Since:

3.0

Version:

$Id: TriangularDistribution.java 18108 2017-10-04 06:45:27Z bignon $

See Also:

Triangular distribution (Wikipedia), Serialized Form

Field Summary
- Fields inherited from class fr.cnes.sirius.patrius.math.distribution.AbstractRealDistribution
  random, SOLVER_DEFAULT_ABSOLUTE_ACCURACY

Constructor Summary

Constructors
Constructor and Description
`TriangularDistribution(double aIn, double cIn, double bIn)` Creates a triangular real distribution using the given lower limit, upper limit, and mode.
`TriangularDistribution(RandomGenerator rng, double aIn, double cIn, double bIn)` Creates a triangular distribution.

Method Summary

All Methods Instance Methods Concrete 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)` The default implementation returns `RealDistribution.getSupportLowerBound()` for `p = 0`, `RealDistribution.getSupportUpperBound()` for `p = 1`.
`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.
`boolean`	`isSupportLowerBoundInclusive()` Returns true if support contains lower bound.
`boolean`	`isSupportUpperBoundInclusive()` Returns true if support contains upper bound.

Methods inherited from class fr.cnes.sirius.patrius.math.distribution.AbstractRealDistribution
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 aIn,
                              double cIn,
                              double bIn)
```
    Creates a triangular real distribution using the given lower limit, upper limit, and mode.
    
    Parameters:
    
    aIn - Lower limit of this distribution (inclusive).
    
    bIn - Upper limit of this distribution (inclusive).
    
    cIn - Mode of this distribution.
    
    Throws:
    
    NumberIsTooLargeException - if a >= b or if c > b.
    
    NumberIsTooSmallException - if c < a.
  - TriangularDistribution
```
public TriangularDistribution(RandomGenerator rng,
                              double aIn,
                              double cIn,
                              double bIn)
```
    Creates a triangular distribution.
    
    Parameters:
    
    rng - Random number generator.
    
    aIn - Lower limit of this distribution (inclusive).
    
    bIn - Upper limit of this distribution (inclusive).
    
    cIn - 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()
```
    Returns true if support contains lower bound.
    
    Returns:
    
    true
  - isSupportUpperBoundInclusive
```
public boolean isSupportUpperBoundInclusive()
```
    Returns true if support contains upper bound.
    
    Returns:
    
    true
  - 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)
```
    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)

Class TriangularDistribution

Field Summary

Fields inherited from class fr.cnes.sirius.patrius.math.distribution.AbstractRealDistribution

Constructor Summary

Method Summary

Methods inherited from class fr.cnes.sirius.patrius.math.distribution.AbstractRealDistribution

Methods inherited from class java.lang.Object

Constructor Detail

TriangularDistribution

TriangularDistribution

Method Detail

getMode

getSolverAbsoluteAccuracy

density

cumulativeProbability

getNumericalMean

getNumericalVariance

getSupportLowerBound

getSupportUpperBound

isSupportLowerBoundInclusive

isSupportUpperBoundInclusive

isSupportConnected

inverseCumulativeProbability