UniformIntDist (Java Libraries for Stochastic Simulation)

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

All Implemented Interfaces:

Distribution
```
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

Constructors
Constructor and Description

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

Constructors
Constructor and Description
`UniformIntDist(int i, int j)` Constructs a discrete uniform distribution over the interval [i, j].

Method Summary

Methods
Modifier and Type	Method and Description
`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.
`static double[]`	`getMaximumLikelihoodEstimate(int[] x, int n)` Deprecated.
`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, which should be a real number in the interval [0, 1].
`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.
`java.lang.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, which should be a real number in the interval [0, 1].
    
    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;)]
  - getMaximumLikelihoodEstimate
```
@Deprecated
public static double[] getMaximumLikelihoodEstimate(int[] x,
                                               int n)
```
    Deprecated.
    
    Same as getMLE.
  - 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 java.lang.String toString()
```
    Overrides:
    
    toString in class java.lang.Object

Class UniformIntDist

Field Summary

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

Constructor Summary

Method Summary

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

Methods inherited from class java.lang.Object

Constructor Detail

UniformIntDist

Method Detail

prob

cdf

barF

inverseFInt

getMean

getVariance

getStandardDeviation

prob

cdf

barF

inverseF

getMLE

getMaximumLikelihoodEstimate

getInstanceFromMLE

getMean

getVariance

getStandardDeviation

getI

getJ

setParams

getParams

toString