TruncatedDist (Java Libraries for Stochastic Simulation)

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

All Implemented Interfaces:

Distribution
```
public class TruncatedDist
extends ContinuousDistribution
```
This container class takes an arbitrary continuous distribution and truncates it to an interval [a, b], where a and b can be finite or infinite. If the original density and distribution function are f and F, the new ones are f^* and F^*, defined by

f^*(x) = f (x)/(F(b) - F(a)) for a <= x <= b
and f^*(x) = 0 and zero elsewhere, and

F^*(x) = F(x)/(F(b) - F(a)) for a <= x <= b.
The inverse distribution function of the truncated distribution is

F^-1*(u) = F^-1(F(a) + (F(b) - F(a))u)
where F^-1 is the inverse distribution function of the original distribution.

Field Summary

Fields
Modifier and Type Field and Description

static int NUMINTERVALS
- Fields inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution
  decPrec

Fields
Modifier and Type	Field and Description
`static int`	`NUMINTERVALS`

Constructor Summary

Constructors
Constructor and Description
`TruncatedDist(ContinuousDistribution dist, double a, double b)` Constructs a new distribution by truncating distribution `dist` to the interval [a, b].

Method Summary

Methods
Modifier and Type	Method and Description
`double`	`barF(double x)` Returns the complementary distribution function.
`double`	`cdf(double x)` Returns the distribution function F(x).
`double`	`density(double x)` Returns an approximation of the mean obtained using the Simpson 1/3 numerical integration, or throws an `UnsupportedOperationException` if a or b are infinite.
`double`	`getA()` Returns the value of a.
`double`	`getArea()` Returns the value of F(b) - F(a), the area under the truncated density function.
`double`	`getB()` Returns the value of b.
`double`	`getFa()` Returns the value of F(a).
`double`	`getFb()` Returns the value of F(b).
`double`	`getMean()` Returns the mean.
`double[]`	`getParams()` Return a table containing the parameters of the current distribution.
`double`	`getStandardDeviation()` Returns the standard deviation.
`double`	`getVariance()` Returns an approximation of the variance obtained using the Simpson 1/3 numerical integration, or throws an `UnsupportedOperationException` if a or b are infinite.
`double`	`inverseF(double u)` Returns the inverse distribution function x = F^-1(u).
`void`	`setParams(ContinuousDistribution dist, double a, double b)` Sets the parameters dist, a and b 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

- Field Detail
  - NUMINTERVALS
```
public static int NUMINTERVALS
```
- Constructor Detail
  - TruncatedDist
```
public TruncatedDist(ContinuousDistribution dist,
             double a,
             double b)
```
    Constructs a new distribution by truncating distribution dist to the interval [a, b]. If a = Double.NEGATIVE_INFINITY, F(a) is assumed to be 0. If b = Double.POSITIVE_INFINITY, F(b) is assumed to be 1.
- Method Detail
  - density
```
public double density(double x)
```
    Returns an approximation of the mean obtained using the Simpson 1/3 numerical integration, or throws an UnsupportedOperationException if a or b are infinite.
    
    Specified by:
    
    density in class ContinuousDistribution
    
    Parameters:
    x - value at which the density is evaluated
    
    Returns:
    density function evaluated at x
    
    Throws:
    
    java.lang.UnsupportedOperationException - the mean of the truncated distribution is unknown
  - 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()
```
    Returns an approximation of the variance obtained using the Simpson 1/3 numerical integration, or throws an UnsupportedOperationException if a or b are infinite.
    
    Specified by:
    
    getVariance in interface Distribution
    
    Overrides:
    
    getVariance in class ContinuousDistribution
    
    Returns:
    the variance
    
    Throws:
    
    java.lang.UnsupportedOperationException - the mean of the truncated distribution is unknown
  - 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
  - getA
```
public double getA()
```
    Returns the value of a.
  - getB
```
public double getB()
```
    Returns the value of b.
  - getFa
```
public double getFa()
```
    Returns the value of F(a).
  - getFb
```
public double getFb()
```
    Returns the value of F(b).
  - getArea
```
public double getArea()
```
    Returns the value of F(b) - F(a), the area under the truncated density function.
  - setParams
```
public void setParams(ContinuousDistribution dist,
             double a,
             double b)
```
    Sets the parameters dist, a and b for this object. See the constructor for details.
  - getParams
```
public double[] getParams()
```
    Return a table containing the parameters of the current distribution. This table is put in order: [a, b, F(a), F(b), F(b) - F(a)].
  - toString
```
public java.lang.String toString()
```
    Returns a String containing information about the current distribution.
    
    Overrides:
    
    toString in class java.lang.Object

Class TruncatedDist

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

Field Detail

NUMINTERVALS

Constructor Detail

TruncatedDist

Method Detail

density

cdf

barF

inverseF

getMean

getVariance

getStandardDeviation

getA

getB

getFa

getFb

getArea

setParams

getParams

toString