umontreal.iro.lecuyer.probdist
Class UniformIntDist

java.lang.Object
  umontreal.iro.lecuyer.probdist.DiscreteDistributionInt
      umontreal.iro.lecuyer.probdist.UniformIntDist

All Implemented Interfaces:

Distribution

Direct Known Subclasses:

ConstantIntDist

public class UniformIntDist
extends DiscreteDistributionInt

Extends the class DiscreteDistributionInt for the discrete uniform distribution over the range [i, j]. Its mass function is given by

p(x) = 1/(j - i + 1) for x = i, i + 1,…, j

and 0 elsewhere. The distribution function is

F(x) = (floor(x) - i + 1)/(j - i + 1) for i <= x <= j

and its inverse is

F^-1(u) = i + (j - i + 1)u for 0 <= u <= 1.

Field Summary

Fields inherited from class umontreal.iro.lecuyer.probdist.DiscreteDistributionInt

EPSILON

Constructor Summary

UniformIntDist(int i, int j)
Constructs a discrete uniform distribution over the interval [i, j].

Method Summary

double	barF(int x) Returns bar(F)(x), the complementary distribution function.
static double	barF(int i, int j, int x) Computes the discrete uniform complementary distribution function bar(F)(x).
double	cdf(int x) Returns the distribution function F evaluated at x (see).
static double	cdf(int i, int j, int x) Computes the discrete uniform distribution function defined in.
int	getI() Returns the parameter i.
static UniformIntDist	getInstanceFromMLE(int[] x, int n) Creates a new instance of a discrete uniform distribution over integers with parameters i and j estimated using the maximum likelihood method based on the n observations x[k], k = 0, 1,…, n - 1.
int	getJ() Returns the parameter j.
double	getMean() Returns the mean of the distribution function.
static double	getMean(int i, int j) Computes and returns the mean E[X] = (i + j)/2 of the discrete uniform distribution.
static double[]	getMLE(int[] x, int n) Estimates the parameters (i, j) of the uniform distribution over integers using the maximum likelihood method, from the n observations x[k], k = 0, 1,…, n - 1.
double[]	getParams() Return a table containing the parameters of the current distribution.
double	getStandardDeviation() Returns the standard deviation of the distribution function.
static double	getStandardDeviation(int i, int j) Computes and returns the standard deviation of the discrete uniform distribution.
double	getVariance() Returns the variance of the distribution function.
static double	getVariance(int i, int j) Computes and returns the variance Var[X] = [(j - i + 1)2 -1]/12 of the discrete uniform distribution.
static int	inverseF(int i, int j, double u) Computes the inverse of the discrete uniform distribution function.
int	inverseFInt(double u) Returns the inverse distribution function F-1(u), where 0 <= u <= 1.
double	prob(int x) Returns p(x), the probability of x.
static double	prob(int i, int j, int x) Computes the discrete uniform probability p(x).
void	setParams(int i, int j) Sets the parameters i and j for this object.
String	toString()

Methods inherited from class umontreal.iro.lecuyer.probdist.DiscreteDistributionInt

barF, cdf, getXinf, getXsup, inverseF

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, wait, wait, wait

Constructor Detail

UniformIntDist

public UniformIntDist(int i,
                      int j)

Constructs a discrete uniform distribution over the interval [i, j].

Method Detail

prob

public double prob(int x)

Description copied from class: DiscreteDistributionInt

Returns p(x), the probability of x.

Specified by:

prob in class DiscreteDistributionInt

Parameters:

x - value at which the mass function must be evaluated

Returns:

the mass function evaluated at x

cdf

public double cdf(int x)

Description copied from class: DiscreteDistributionInt

Returns the distribution function F evaluated at x (see).

Specified by:

cdf in class DiscreteDistributionInt

Parameters:

x - value at which the distribution function must be evaluated

Returns:

the distribution function evaluated at x

barF

public double barF(int x)

Description copied from class: DiscreteDistributionInt

Returns bar(F)(x), the complementary distribution function. See the WARNING above.

Overrides:

barF in class DiscreteDistributionInt

Parameters:

x - value at which the complementary distribution function must be evaluated

Returns:

the complementary distribution function evaluated at x

inverseFInt

public int inverseFInt(double u)

Description copied from class: DiscreteDistributionInt

Returns the inverse distribution function F^-1(u), where 0 <= u <= 1. The default implementation uses binary search.

Overrides:

inverseFInt in class DiscreteDistributionInt

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.

prob

public static double prob(int i,
                          int j,
                          int x)

Computes the discrete uniform probability p(x).

cdf

public static double cdf(int i,
                         int j,
                         int x)

Computes the discrete uniform distribution function defined in.

barF

public static double barF(int i,
                          int j,
                          int x)

Computes the discrete uniform complementary distribution function bar(F)(x). WARNING: The complementary distribution function is defined as bar(F)(x) = P[X >= x].

inverseF

public static int inverseF(int i,
                           int j,
                           double u)

Computes the inverse of the discrete uniform distribution function.

getMLE

public static double[] getMLE(int[] x,
                              int n)

Estimates the parameters (i, j) of the uniform distribution over integers using the maximum likelihood method, from the n observations x[k], k = 0, 1,…, n - 1. The estimates are returned in a two-element array, in regular order: [i, j].

Parameters:

x - the list of observations used to evaluate parameters

n - the number of observations used to evaluate parameters

Returns:

returns the parameters [ hat(ı), hat(&jnodot;)]

getInstanceFromMLE

public static UniformIntDist getInstanceFromMLE(int[] x,
                                                int n)

Creates a new instance of a discrete uniform distribution over integers with parameters i and j estimated using the maximum likelihood method based on the n observations x[k], k = 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(int i,
                             int j)

Computes and returns the mean E[X] = (i + j)/2 of the discrete uniform distribution.

Returns:

the mean of the discrete uniform distribution

getVariance

public static double getVariance(int i,
                                 int j)

Computes and returns the variance Var[X] = [(j - i + 1)² -1]/12 of the discrete uniform distribution.

Returns:

the variance of the discrete uniform distribution

getStandardDeviation

public static double getStandardDeviation(int i,
                                          int j)

Computes and returns the standard deviation of the discrete uniform distribution.

Returns:

the standard deviation of the discrete uniform distribution

getI

public int getI()

Returns the parameter i.

getJ

public int getJ()

Returns the parameter j.

setParams

public void setParams(int i,
                      int j)

Sets the parameters i and j for this object.

getParams

public double[] getParams()

Return a table containing the parameters of the current distribution. This table is put in regular order: [i, j].

toString

public String toString()

Overrides:

toString in class Object