SSJ
V. 2.6.

## 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 UniformDistextends 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.