SSJ
V. 1.2.5.

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 bar(F)(x) = 1 - F(x).
static double barF(double a, double b, double x)
          Computes the uniform complementary distribution function bar(F)(x).
 double cdf(double x)
          Computes and 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 of X 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 in table x[i], i = 0, 1,…, n - 1.
static double[] getMaximumLikelihoodEstimate(double[] x, int n)
          Estimates and returns the parameters [hat(a), hat(b)] of the uniform distribution using the maximum likelihood method based on the n observations in table x[i], i = 0, 1,…, n - 1.
 double getMean()
          Returns the mean of the distribution function.
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.
 double getStandardDeviation()
          Returns the standard deviation of the distribution function.
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 of the distribution function.
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)
          Computes and returns the inverse distribution function F-1(u), defined in.
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.
 
Methods inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution
inverseBisection, inverseBrent
 
Methods inherited from class java.lang.Object
equals, getClass, hashCode, notify, notifyAll, toString, 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 of X 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
Computes and 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 interface: Distribution
Returns 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 interface: Distribution
Computes and returns the inverse distribution function F-1(u), defined in.

Specified by:
inverseF in interface Distribution
Overrides:
inverseF in class ContinuousDistribution
Parameters:
u - value in the interval (0, 1) for which the inverse distribution function is evaluated
Returns:
the inverse distribution function evaluated at u

getMean

public double getMean()
Description copied from interface: Distribution
Returns the mean of the distribution function.


getVariance

public double getVariance()
Description copied from interface: Distribution
Returns the variance of the distribution function.


getStandardDeviation

public double getStandardDeviation()
Description copied from interface: Distribution
Returns the standard deviation of the distribution function.


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.


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 in table 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

getMaximumLikelihoodEstimate

public static double[] getMaximumLikelihoodEstimate(double[] x,
                                                    int n)
Estimates and returns the parameters [hat(a), hat(b)] of the uniform distribution using the maximum likelihood method based on the n observations in table 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
Returns:
returns the parameters [hat(a), hat(b)]

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.


SSJ
V. 1.2.5.

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