org.apache.commons.math3.distribution
Class UniformRealDistribution

java.lang.Object
  org.apache.commons.math3.distribution.AbstractRealDistribution
      org.apache.commons.math3.distribution.UniformRealDistribution

All Implemented Interfaces:

Serializable, RealDistribution

public class UniformRealDistribution
extends AbstractRealDistribution

Implementation of the uniform real distribution.

Since:

3.0

Version:

$Id: UniformRealDistribution.java 1462020 2013-03-28 10:24:45Z luc $

See Also:

Uniform distribution (continuous), at Wikipedia, Serialized Form

DEFAULT_INVERSE_ABSOLUTE_ACCURACY

@Deprecated
public static final double DEFAULT_INVERSE_ABSOLUTE_ACCURACY

Deprecated. as of 3.2 not used anymore, will be removed in 4.0

Default inverse cumulative probability accuracy.

See Also:

Constant Field Values

UniformRealDistribution

public UniformRealDistribution()

Create a standard uniform real distribution with lower bound (inclusive) equal to zero and upper bound (exclusive) equal to one.

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

@Deprecated
public UniformRealDistribution(double lower,
                                          double upper,
                                          double inverseCumAccuracy)
                        throws NumberIsTooLargeException

Deprecated. as of 3.2, inverse CDF is now calculated analytically, use UniformRealDistribution(double, double) instead.

Create a uniform distribution.

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

@Deprecated
public UniformRealDistribution(RandomGenerator rng,
                                          double lower,
                                          double upper,
                                          double inverseCumAccuracy)

Deprecated. as of 3.2, inverse CDF is now calculated analytically, use UniformRealDistribution(RandomGenerator, double, double) instead.

Creates a uniform distribution.

Parameters:

rng - Random number generator.

lower - Lower bound of this distribution (inclusive).

upper - Upper bound of this distribution (exclusive).

inverseCumAccuracy - Inverse cumulative probability accuracy.

Throws:

NumberIsTooLargeException - if lower >= upper.

Since:

3.1

UniformRealDistribution

public UniformRealDistribution(RandomGenerator rng,
                               double lower,
                               double upper)
                        throws NumberIsTooLargeException

Creates a uniform distribution.

Parameters:

rng - Random number generator.

lower - Lower bound of this distribution (inclusive).

upper - Upper bound of this distribution (exclusive).

Throws:

NumberIsTooLargeException - if lower >= upper.

Since:

3.1

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

inverseCumulativeProbability

public double inverseCumulativeProbability(double p)
                                    throws OutOfRangeException

Description copied from class: AbstractRealDistribution

Computes the quantile function of this distribution. For a random variable X distributed according to this distribution, the returned value is

• inf{x in R | P(X<=x) >= p} for 0 < p <= 1,
• inf{x in R | P(X<=x) > 0} for p = 0.

The default implementation returns

• RealDistribution.getSupportLowerBound() for p = 0,
• RealDistribution.getSupportUpperBound() for p = 1.

Specified by:

inverseCumulativeProbability in interface RealDistribution

Overrides:

inverseCumulativeProbability in class AbstractRealDistribution

Parameters:

p - the cumulative probability

Returns:

the smallest p-quantile of this distribution (largest 0-quantile for p = 0)

Throws:

OutOfRangeException - if p < 0 or p > 1

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()

Whether or not the lower bound of support is in the domain of the density function. Returns true iff getSupporLowerBound() is finite and density(getSupportLowerBound()) returns a non-NaN, non-infinite value.

Returns:

true if the lower bound of support is finite and the density function returns a non-NaN, non-infinite value there

isSupportUpperBoundInclusive

public boolean isSupportUpperBoundInclusive()

Whether or not the upper bound of support is in the domain of the density function. Returns true iff getSupportUpperBound() is finite and density(getSupportUpperBound()) returns a non-NaN, non-infinite value.

Returns:

true if the upper bound of support is finite and the density function returns a non-NaN, non-infinite value there

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.