SSJ
V. 1.2.5.

umontreal.iro.lecuyer.probdist
Class TriangularDist

java.lang.Object
  extended by umontreal.iro.lecuyer.probdist.ContinuousDistribution
      extended by 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
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
 double barF(double x)
          Returns bar(F)(x) = 1 - F(x).
static double barF(double a, double b, double m, double x)
          Computes the complementary distribution function.
 double cdf(double x)
          Computes and 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 of X 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 of the distribution function.
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 getStandardDeviation()
          Returns the standard deviation of the distribution function.
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 of the distribution function.
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)
          Computes and returns the inverse distribution function F-1(u), defined in.
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.
 
Methods inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution
inverseBisection, inverseBrent
 
Methods inherited from class java.lang.Object
equals, getClass, hashCode, notify, notifyAll, toString, 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 of X 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
Computes and 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 interface: Distribution
Returns 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 interface: Distribution
Computes and returns the inverse distribution function F-1(u), defined in.

Specified by:
inverseF in interface Distribution
Overrides:
inverseF in class ContinuousDistribution
Parameters:
u - value in the interval (0, 1) for which the inverse distribution function is evaluated
Returns:
the inverse distribution function evaluated at u

getMean

public double getMean()
Description copied from interface: Distribution
Returns the mean of the distribution function.


getVariance

public double getVariance()
Description copied from interface: Distribution
Returns the variance of the distribution function.


getStandardDeviation

public double getStandardDeviation()
Description copied from interface: Distribution
Returns the standard deviation of the distribution function.


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.


SSJ
V. 1.2.5.

To submit a bug or ask questions, send an e-mail to Pierre L'Ecuyer.