org.apache.commons.math3.distribution

## Class UniformRealDistribution

• ### Field Summary

Fields
Modifier and Type Field and Description
`static double` `DEFAULT_INVERSE_ABSOLUTE_ACCURACY`
Default inverse cumulative probability accuracy.
• ### Fields inherited from class org.apache.commons.math3.distribution.AbstractRealDistribution

`randomData, SOLVER_DEFAULT_ABSOLUTE_ACCURACY`
• ### Constructor Summary

Constructors
Constructor and Description
`UniformRealDistribution()`
Create a standard uniform real distribution with lower bound (inclusive) equal to zero and upper bound (exclusive) equal to one.
```UniformRealDistribution(double lower, double upper)```
Create a uniform real distribution using the given lower and upper bounds.
```UniformRealDistribution(double lower, double upper, double inverseCumAccuracy)```
Create a normal distribution using the given mean, standard deviation and inverse cumulative distribution accuracy.
• ### Method Summary

Methods
Modifier and Type Method and Description
`double` `cumulativeProbability(double x)`
For a random variable `X` whose values are distributed according to this distribution, this method returns `P(X <= x)`.
`double` `density(double x)`
Returns the probability density function (PDF) of this distribution evaluated at the specified point `x`.
`double` `getNumericalMean()`
Use this method to get the numerical value of the mean of this distribution.
`double` `getNumericalVariance()`
Use this method to get the numerical value of the variance of this distribution.
`protected double` `getSolverAbsoluteAccuracy()`
Returns the solver absolute accuracy for inverse cumulative computation.
`double` `getSupportLowerBound()`
Access the lower bound of the support.
`double` `getSupportUpperBound()`
Access the upper bound of the support.
`boolean` `isSupportConnected()`
Use this method to get information about whether the support is connected, i.e.
`boolean` `isSupportLowerBoundInclusive()`
Use this method to get information about whether the lower bound of the support is inclusive or not.
`boolean` `isSupportUpperBoundInclusive()`
Use this method to get information about whether the upper bound of the support is inclusive or not.
`double` `probability(double x)`
For a random variable `X` whose values are distributed according to this distribution, this method returns `P(X = x)`.
`double` `sample()`
Generate a random value sampled from this distribution.
• ### Methods inherited from class org.apache.commons.math3.distribution.AbstractRealDistribution

`cumulativeProbability, inverseCumulativeProbability, reseedRandomGenerator, sample`
• ### Methods inherited from class java.lang.Object

`clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait`
• ### Field Detail

• #### DEFAULT_INVERSE_ABSOLUTE_ACCURACY

`public static final double DEFAULT_INVERSE_ABSOLUTE_ACCURACY`
Default inverse cumulative probability accuracy.
See Also:
Constant Field Values
• ### Constructor Detail

• #### UniformRealDistribution

```public UniformRealDistribution(double lower,
double upper)
throws NumberIsTooLargeException```
Create a uniform real distribution using the given lower and upper bounds.
Parameters:
`lower` - Lower bound of this distribution (inclusive).
`upper` - Upper bound of this distribution (exclusive).
Throws:
`NumberIsTooLargeException` - if `lower >= upper`.
• #### UniformRealDistribution

```public UniformRealDistribution(double lower,
double upper,
double inverseCumAccuracy)
throws NumberIsTooLargeException```
Create a normal distribution using the given mean, standard deviation and inverse cumulative distribution accuracy.
Parameters:
`lower` - Lower bound of this distribution (inclusive).
`upper` - Upper bound of this distribution (exclusive).
`inverseCumAccuracy` - Inverse cumulative probability accuracy.
Throws:
`NumberIsTooLargeException` - if `lower >= upper`.
• #### UniformRealDistribution

`public UniformRealDistribution()`
Create a standard uniform real distribution with lower bound (inclusive) equal to zero and upper bound (exclusive) equal to one.
• ### Method Detail

• #### probability

`public double probability(double x)`
For a random variable `X` whose values are distributed according to this distribution, this method returns `P(X = x)`. In other words, this method represents the probability mass function (PMF) for the distribution. For this distribution `P(X = x)` always evaluates to 0.
Parameters:
`x` - the point at which the PMF is evaluated
Returns:
0
• #### density

`public double density(double x)`
Returns the probability density function (PDF) of this distribution evaluated at the specified point `x`. In general, the PDF is the derivative of the `CDF`. If the derivative does not exist at `x`, then an appropriate replacement should be returned, e.g. `Double.POSITIVE_INFINITY`, `Double.NaN`, or the limit inferior or limit superior of the difference quotient.
Parameters:
`x` - the point at which the PDF is evaluated
Returns:
the value of the probability density function at point `x`
• #### cumulativeProbability

`public double cumulativeProbability(double x)`
For a random variable `X` whose values are distributed according to this distribution, this method returns `P(X <= x)`. In other words, this method represents the (cumulative) distribution function (CDF) for this distribution.
Parameters:
`x` - the point at which the CDF is evaluated
Returns:
the probability that a random variable with this distribution takes a value less than or equal to `x`
• #### getSolverAbsoluteAccuracy

`protected double getSolverAbsoluteAccuracy()`
Returns the solver absolute accuracy for inverse cumulative computation. You can override this method in order to use a Brent solver with an absolute accuracy different from the default.
Overrides:
`getSolverAbsoluteAccuracy` in class `AbstractRealDistribution`
Returns:
the maximum absolute error in inverse cumulative probability estimates
• #### getNumericalMean

`public double getNumericalMean()`
Use this method to get the numerical value of the mean of this distribution. For lower bound `lower` and upper bound `upper`, the mean is `0.5 * (lower + upper)`.
Returns:
the mean or `Double.NaN` if it is not defined
• #### getNumericalVariance

`public double getNumericalVariance()`
Use this method to get the numerical value of the variance of this distribution. For lower bound `lower` and upper bound `upper`, the variance is `(upper - lower)^2 / 12`.
Returns:
the variance (possibly `Double.POSITIVE_INFINITY` as for certain cases in `TDistribution`) or `Double.NaN` if it is not defined
• #### getSupportLowerBound

`public double getSupportLowerBound()`
Access the lower bound of the support. This method must return the same value as `inverseCumulativeProbability(0)`. In other words, this method must return

`inf {x in R | P(X <= x) > 0}`.

The lower bound of the support is equal to the lower bound parameter of the distribution.
Returns:
lower bound of the support
• #### getSupportUpperBound

`public double getSupportUpperBound()`
Access the upper bound of the support. This method must return the same value as `inverseCumulativeProbability(1)`. In other words, this method must return

`inf {x in R | P(X <= x) = 1}`.

The upper bound of the support is equal to the upper bound parameter of the distribution.
Returns:
upper bound of the support
• #### isSupportLowerBoundInclusive

`public boolean isSupportLowerBoundInclusive()`
Use this method to get information about whether the lower bound of the support is inclusive or not.
Returns:
whether the lower bound of the support is inclusive or not
• #### isSupportUpperBoundInclusive

`public boolean isSupportUpperBoundInclusive()`
Use this method to get information about whether the upper bound of the support is inclusive or not.
Returns:
whether the upper bound of the support is inclusive or not
• #### isSupportConnected

`public boolean isSupportConnected()`
Use this method to get information about whether the support is connected, i.e. whether all values between the lower and upper bound of the support are included in the support. The support of this distribution is connected.
Returns:
`true`
• #### sample

`public double sample()`
Generate a random value sampled from this distribution. The default implementation uses the inversion method.
Specified by:
`sample` in interface `RealDistribution`
Overrides:
`sample` in class `AbstractRealDistribution`
Returns:
a random value.

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