TriangularDist (Java Libraries for Stochastic Simulation)

java.lang.Object
- umontreal.iro.lecuyer.probdist.ContinuousDistribution
- - umontreal.iro.lecuyer.probdist.TriangularDist

All Implemented Interfaces:: Distribution

public class TriangularDist
extends ContinuousDistribution

Extends the class ContinuousDistribution for the triangular distribution with domain [a, b] and mode (or shape parameter) m, where a <= m <= b. The density function is

f (x) =	2(x - a)/[(b - a)(m - a)]	for a <= x <= m,
f (x) =	2(b - x)/[(b - a)(b - m)]	for m <= x <= b,
f (x) =	0	elsewhere,

the distribution function is

F(x) =	0	for x < a,
F(x) =	(x - a)²/[(b - a)(m - a)]	if a <= x <= m,
F(x) =	1 - (b - x)²/[(b - a)(b - m)]	if m <= x <= b,
F(x) =	1	for x > b,

and the inverse distribution function is given by

F^-1(u) =	a + ((b - a)(m - a)u)^1/2	if 0 <= u <= (m - a)/(b - a),
F^-1(u) =	b - ((b - a)(b - m)(1 - u))^1/2	if (m - a)/(b - a <= u <= 1.

Field Summary
- Fields inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution
  decPrec

Constructor Summary

Constructors
Constructor and Description
`TriangularDist()` Constructs a `TriangularDist` object with default parameters a = 0, b = 1, and m = 0.5.
`TriangularDist(double m)` Constructs a `TriangularDist` object with parameters a = 0 , b = 1 and m = `m`.
`TriangularDist(double a, double b, double m)` Constructs a `TriangularDist` object with parameters a, b and m.

Method Summary

Methods
Modifier and Type	Method and Description
`double`	`barF(double x)` Returns the complementary distribution function.
`static double`	`barF(double a, double b, double m, double x)` Computes the complementary distribution function.
`double`	`cdf(double x)` Returns the distribution function F(x).
`static double`	`cdf(double a, double b, double m, double x)` Computes the distribution function.
`double`	`density(double x)` Returns f (x), the density evaluated at x.
`static double`	`density(double a, double b, double m, double x)` Computes the density function.
`double`	`getA()` Returns the value of a for this object.
`double`	`getB()` Returns the value of b for this object.
`double`	`getM()` Returns the value of m for this object.
`double`	`getMean()` Returns the mean.
`static double`	`getMean(double a, double b, double m)` Computes and returns the mean E[X] = (a + b + m)/3 of the triangular distribution with parameters a, b, m.
`double[]`	`getParams()` Return a table containing the parameters of the current distribution.
`double`	`getStandardDeviation()` Returns the standard deviation.
`static double`	`getStandardDeviation(double a, double b, double m)` Computes and returns the standard deviation of the triangular distribution with parameters a, b, m.
`double`	`getVariance()` Returns the variance.
`static double`	`getVariance(double a, double b, double m)` Computes and returns the variance Var[X] = (a² + b² + m² - ab - am - bm)/18 of the triangular distribution with parameters a, b, m.
`double`	`inverseF(double u)` Returns the inverse distribution function x = F^-1(u).
`static double`	`inverseF(double a, double b, double m, double u)` Computes the inverse distribution function.
`void`	`setParams(double a, double b, double m)` Sets the value of the parameters a, b and m for this object.
`java.lang.String`	`toString()` Returns a `String` containing information about the current distribution.

Methods inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution
getXinf, getXsup, inverseBisection, inverseBrent, setXinf, setXsup

Methods inherited from class java.lang.Object
equals, getClass, hashCode, notify, notifyAll, wait, wait, wait

- Constructor Detail
  - TriangularDist
```
public TriangularDist()
```
    Constructs a TriangularDist object with default parameters a = 0, b = 1, and m = 0.5.
  - TriangularDist
```
public TriangularDist(double m)
```
    Constructs a TriangularDist object with parameters a = 0 , b = 1 and m = m.
  - TriangularDist
```
public TriangularDist(double a,
              double b,
              double m)
```
    Constructs a TriangularDist object with parameters a, b and m.
- Method Detail
  - density
```
public double density(double x)
```
    Description copied from class: ContinuousDistribution
    
    Returns f (x), the density evaluated at x.
    
    Specified by:
    
    density in class ContinuousDistribution
    
    Parameters:
    x - value at which the density is evaluated
    
    Returns:
    density function evaluated at x
  - cdf
```
public double cdf(double x)
```
    Description copied from interface: Distribution
    
    Returns the distribution function F(x).
    
    Parameters:
    x - value at which the distribution function is evaluated
    
    Returns:
    distribution function evaluated at x
  - barF
```
public double barF(double x)
```
    Description copied from class: ContinuousDistribution
    
    Returns the complementary distribution function. The default implementation computes bar(F)(x) = 1 - F(x).
    
    Specified by:
    
    barF in interface Distribution
    
    Overrides:
    
    barF in class ContinuousDistribution
    
    Parameters:
    x - value at which the complementary distribution function is evaluated
    
    Returns:
    complementary distribution function evaluated at x
  - inverseF
```
public double inverseF(double u)
```
    Description copied from class: ContinuousDistribution
    
    Returns the inverse distribution function x = F^-1(u). Restrictions: u∈[0, 1].
    
    Specified by:
    
    inverseF in interface Distribution
    
    Overrides:
    
    inverseF in class ContinuousDistribution
    
    Parameters:
    u - value at which the inverse distribution function is evaluated
    
    Returns:
    the inverse distribution function evaluated at u
  - getMean
```
public double getMean()
```
    Description copied from class: ContinuousDistribution
    
    Returns the mean.
    
    Specified by:
    
    getMean in interface Distribution
    
    Overrides:
    
    getMean in class ContinuousDistribution
    
    Returns:
    the mean
  - getVariance
```
public double getVariance()
```
    Description copied from class: ContinuousDistribution
    
    Returns the variance.
    
    Specified by:
    
    getVariance in interface Distribution
    
    Overrides:
    
    getVariance in class ContinuousDistribution
    
    Returns:
    the variance
  - getStandardDeviation
```
public double getStandardDeviation()
```
    Description copied from class: ContinuousDistribution
    
    Returns the standard deviation.
    
    Specified by:
    
    getStandardDeviation in interface Distribution
    
    Overrides:
    
    getStandardDeviation in class ContinuousDistribution
    
    Returns:
    the standard deviation
  - density
```
public static double density(double a,
             double b,
             double m,
             double x)
```
    Computes the density function.
  - cdf
```
public static double cdf(double a,
         double b,
         double m,
         double x)
```
    Computes the distribution function.
  - barF
```
public static double barF(double a,
          double b,
          double m,
          double x)
```
    Computes the complementary distribution function.
  - inverseF
```
public static double inverseF(double a,
              double b,
              double m,
              double u)
```
    Computes the inverse distribution function.
  - getMean
```
public static double getMean(double a,
             double b,
             double m)
```
    Computes and returns the mean E[X] = (a + b + m)/3 of the triangular distribution with parameters a, b, m.
    
    Returns:
    the mean of the triangular distribution
  - getVariance
```
public static double getVariance(double a,
                 double b,
                 double m)
```
    Computes and returns the variance Var[X] = (a² + b² + m² - ab - am - bm)/18 of the triangular distribution with parameters a, b, m.
    
    Returns:
    the variance of the triangular distribution
  - getStandardDeviation
```
public static double getStandardDeviation(double a,
                          double b,
                          double m)
```
    Computes and returns the standard deviation of the triangular distribution with parameters a, b, m.
    
    Returns:
    the standard deviation of the triangular distribution
  - getA
```
public double getA()
```
    Returns the value of a for this object.
  - getB
```
public double getB()
```
    Returns the value of b for this object.
  - getM
```
public double getM()
```
    Returns the value of m for this object.
  - setParams
```
public void setParams(double a,
             double b,
             double m)
```
    Sets the value of the parameters a, b and m for this object.
  - getParams
```
public double[] getParams()
```
    Return a table containing the parameters of the current distribution. This table is put in regular order: [a, b, m].
  - toString
```
public java.lang.String toString()
```
    Returns a String containing information about the current distribution.
    
    Overrides:
    
    toString in class java.lang.Object

Class TriangularDist

Field Summary

Fields inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution

Constructor Summary

Method Summary

Methods inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution

Methods inherited from class java.lang.Object

Constructor Detail

TriangularDist

TriangularDist

TriangularDist

Method Detail

density

cdf

barF

inverseF

getMean

getVariance

getStandardDeviation

density

cdf

barF

inverseF

getMean

getVariance

getStandardDeviation

getA

getB

getM

setParams

getParams

toString