SSJ
V. 2.6.

## umontreal.iro.lecuyer.probdist Class TriangularDist

```java.lang.Object
umontreal.iro.lecuyer.probdist.ContinuousDistribution
umontreal.iro.lecuyer.probdist.TriangularDist
```
All Implemented Interfaces:
Distribution

`public class TriangularDistextends 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.