umontreal.iro.lecuyer.probdist

Class UniformDist

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

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.
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)]

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