SSJ
V. 2.6.

umontreal.iro.lecuyer.probdist
Class UniformDist

java.lang.Object
  extended by umontreal.iro.lecuyer.probdist.ContinuousDistribution
      extended by 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
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
 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.
 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.
 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)]

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 String toString()
Overrides:
toString in class Object

SSJ
V. 2.6.

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