UniformDist (Java Libraries for Stochastic Simulation)

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

All Implemented Interfaces:

Distribution
```
public class UniformDist
extends ContinuousDistribution
```
Extends the class ContinuousDistribution for the uniform distribution over the interval [a, b]. Its density is

f (x) = 1/(b - a)         for a <= x <= b
and 0 elsewhere. The distribution function is

F(x) = (x - a)/(b - a)         for a <= x <= b
and its inverse is

F^-1(u) = a + (b - a)u        for 0 <= u <= 1.

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

Constructor Summary

Constructors
Constructor and Description
`UniformDist()` Constructs a uniform distribution over the interval (a, b) = (0, 1).
`UniformDist(double a, double b)` Constructs a uniform distribution over the interval (a, b).

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 x)` Computes the uniform complementary distribution function bar(F)(x).
`double`	`cdf(double x)` Returns the distribution function F(x).
`static double`	`cdf(double a, double b, double x)` Computes the uniform distribution function as in.
`double`	`density(double x)` Returns f (x), the density evaluated at x.
`static double`	`density(double a, double b, double x)` Computes the uniform density function f (x).
`double`	`getA()` Returns the parameter a.
`double`	`getB()` Returns the parameter b.
`static UniformDist`	`getInstanceFromMLE(double[] x, int n)` Creates a new instance of a uniform distribution with parameters a and b estimated using the maximum likelihood method based on the n observations x[i], i = 0, 1,…, n - 1.
`static double[]`	`getMaximumLikelihoodEstimate(double[] x, int n)` Deprecated.
`double`	`getMean()` Returns the mean.
`static double`	`getMean(double a, double b)` Computes and returns the mean E[X] = (a + b)/2 of the uniform distribution with parameters a and b.
`static double[]`	`getMLE(double[] x, int n)` Estimates the parameter (a, b) of the uniform 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)` Computes and returns the standard deviation of the uniform distribution with parameters a and b.
`double`	`getVariance()` Returns the variance.
`static double`	`getVariance(double a, double b)` Computes and returns the variance Var[X] = (b - a)²/12 of the uniform distribution with parameters a and b.
`double`	`inverseF(double u)` Returns the inverse distribution function x = F^-1(u).
`static double`	`inverseF(double a, double b, double u)` Computes the inverse of the uniform distribution function.
`void`	`setParams(double a, double b)` Sets the parameters a and b for this object.
`java.lang.String`	`toString()`

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
  - UniformDist
```
public UniformDist()
```
    Constructs a uniform distribution over the interval (a, b) = (0, 1).
  - UniformDist
```
public UniformDist(double a,
           double b)
```
    Constructs a uniform distribution over the interval (a, b).
- 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 x)
```
    Computes the uniform density function f (x).
  - cdf
```
public static double cdf(double a,
         double b,
         double x)
```
    Computes the uniform distribution function as in.
  - barF
```
public static double barF(double a,
          double b,
          double x)
```
    Computes the uniform complementary distribution function bar(F)(x).
  - inverseF
```
public static double inverseF(double a,
              double b,
              double u)
```
    Computes the inverse of the uniform distribution function.
  - getMLE
```
public static double[] getMLE(double[] x,
              int n)
```
    Estimates the parameter (a, b) of the uniform distribution using the maximum likelihood method, from the n observations x[i], i = 0, 1,…, n - 1. The estimates are returned in a two-element array, in regular order: [a, b].
    
    Parameters:
    x - the list of observations used to evaluate parameters
    n - the number of observations used to evaluate parameters
    
    Returns:
    returns the parameters [hat(a), hat(b)]
  - getMaximumLikelihoodEstimate
```
@Deprecated
public static double[] getMaximumLikelihoodEstimate(double[] x,
                                               int n)
```
    Deprecated.
    
    Same as getMLE.
  - getInstanceFromMLE
```
public static UniformDist getInstanceFromMLE(double[] x,
                             int n)
```
    Creates a new instance of a uniform distribution with parameters a and b estimated using the maximum likelihood method based on the n observations x[i], i = 0, 1,…, n - 1.
    
    Parameters:
    x - the list of observations to use to evaluate parameters
    n - the number of observations to use to evaluate parameters
  - getMean
```
public static double getMean(double a,
             double b)
```
    Computes and returns the mean E[X] = (a + b)/2 of the uniform distribution with parameters a and b.
    
    Returns:
    the mean of the uniform distribution E[X] = (a + b)/2
  - getVariance
```
public static double getVariance(double a,
                 double b)
```
    Computes and returns the variance Var[X] = (b - a)²/12 of the uniform distribution with parameters a and b.
    
    Returns:
    the variance of the uniform distribution Var[X] = (b - a)²/12
  - getStandardDeviation
```
public static double getStandardDeviation(double a,
                          double b)
```
    Computes and returns the standard deviation of the uniform distribution with parameters a and b.
    
    Returns:
    the standard deviation of the uniform distribution
  - getA
```
public double getA()
```
    Returns the parameter a.
  - getB
```
public double getB()
```
    Returns the parameter b.
  - setParams
```
public void setParams(double a,
             double b)
```
    Sets the parameters a and b 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].
  - toString
```
public java.lang.String toString()
```
    Overrides:
    
    toString in class java.lang.Object

Class UniformDist

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

UniformDist

UniformDist

Method Detail

density

cdf

barF

inverseF

getMean

getVariance

getStandardDeviation

density

cdf

barF

inverseF

getMLE

getMaximumLikelihoodEstimate

getInstanceFromMLE

getMean

getVariance

getStandardDeviation

getA

getB

setParams

getParams

toString