SSJ
V. 2.6.

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 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.
static TriangularDist getInstanceFromMLE(double[] x, int n, double a, double b)
          Creates a new instance of a triangular distribution with parameters a and b.
 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.
static double[] getMLE(double[] x, int n, double a, double b)
          Estimates the parameter m of the triangular distribution using the maximum likelihood method, from the n observations x[i], i = 0, 1,…, n - 1.
 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.
 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.


getMLE

public static double[] getMLE(double[] x,
                              int n,
                              double a,
                              double b)
Estimates the parameter m of the triangular distribution using the maximum likelihood method, from the n observations x[i], i = 0, 1,…, n - 1. The estimated parameter is returned in a one-element array: [hat(m)]. See.

Parameters:
x - the list of observations used to evaluate parameters
n - the number of observations used to evaluate parameters
a - lower limit of range
b - upper limit of range
Returns:
returns the parameter [m]

getInstanceFromMLE

public static TriangularDist getInstanceFromMLE(double[] x,
                                                int n,
                                                double a,
                                                double b)
Creates a new instance of a triangular distribution with parameters a and b. m is estimated using the maximum likelihood method based on the n observations x[i], i = 0, 1,…, n - 1.

Parameters:
x - the list of observations used to evaluate parameters
n - the number of observations used to evaluate parameters
a - lower limit of range
b - upper limit of range

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 String toString()
Returns a String containing information about the current distribution.

Overrides:
toString in class Object

SSJ
V. 2.6.

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