org.apache.commons.math3.distribution

## Class AbstractRealDistribution

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

All Implemented Interfaces:
  Serializable, RealDistribution

Direct Known Subclasses:
  BetaDistribution, CauchyDistribution, ChiSquaredDistribution, EmpiricalDistribution, ExponentialDistribution, FDistribution, GammaDistribution, LogNormalDistribution, NormalDistribution, TDistribution, TriangularDistribution, UniformRealDistribution, WeibullDistribution

    public abstract class AbstractRealDistribution
    extends Object
    implements RealDistribution, Serializable

Base class for probability distributions on the reals. Default implementations are provided for some of the methods that do not vary from distribution to distribution.

Since:
  3.0
Version:
  $Id: AbstractRealDistribution.java 1422195 2012-12-15 06:45:18Z psteitz $
See Also:
  Serialized Form

### Field Summary

Fields
`protected RandomGenerator` `random` RNG instance used to generate samples from the distribution.
`protected RandomDataImpl` `randomData` Deprecated. As of 3.1, to be removed in 4.0. Please use the `random` instance variable instead.
`private static long` `serialVersionUID` Serializable version identifier
`static double` `SOLVER_DEFAULT_ABSOLUTE_ACCURACY` Default accuracy.
`private double` `solverAbsoluteAccuracy` Solver absolute accuracy for inverse cumulative computation

### Constructor Summary

Constructors
`protected` `AbstractRealDistribution()` Deprecated. As of 3.1, to be removed in 4.0. Please use `AbstractRealDistribution(RandomGenerator)` instead.
`protected` `AbstractRealDistribution(RandomGenerator rng)`

### Method Summary

Methods
`double` `cumulativeProbability(double x0, double x1)` Deprecated. As of 3.1 (to be removed in 4.0). Please use `probability(double,double)` instead.
`protected double` `getSolverAbsoluteAccuracy()` Returns the solver absolute accuracy for inverse cumulative computation.
`double` `inverseCumulativeProbability(double p)` Computes the quantile function of this distribution.
`double` `probability(double x)` For a random variable `X` whose values are distributed according to this distribution, this method returns `P(X = x)`.
`double` `probability(double x0, double x1)` For a random variable `X` whose values are distributed according to this distribution, this method returns `P(x0 < X <= x1)`.
`void` `reseedRandomGenerator(long seed)` Reseed the random generator used to generate samples.
`double` `sample()` Generate a random value sampled from this distribution.
`double[]` `sample(int sampleSize)` Generate a random sample from the distribution.

### Methods inherited from class java.lang.Object

`clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait`

### Methods inherited from interface org.apache.commons.math3.distribution.RealDistribution

`cumulativeProbability, density, getNumericalMean, getNumericalVariance, getSupportLowerBound, getSupportUpperBound, isSupportConnected, isSupportLowerBoundInclusive, isSupportUpperBoundInclusive`

### Field Detail

#### SOLVER_DEFAULT_ABSOLUTE_ACCURACY

    public static final double SOLVER_DEFAULT_ABSOLUTE_ACCURACY

Default accuracy.

See Also:
  Constant Field Values

#### serialVersionUID

    private static final long serialVersionUID

Serializable version identifier

See Also:
  Constant Field Values

#### randomData

    @Deprecated
    protected RandomDataImpl randomData

Deprecated. As of 3.1, to be removed in 4.0. Please use the `random` instance variable instead.
RandomData instance used to generate samples from the distribution.

#### random

    protected final RandomGenerator random

RNG instance used to generate samples from the distribution.

Since:
  3.1

#### solverAbsoluteAccuracy

    private double solverAbsoluteAccuracy

Solver absolute accuracy for inverse cumulative computation

### Constructor Detail

#### AbstractRealDistribution

    @Deprecated
    protected AbstractRealDistribution()

Deprecated. As of 3.1, to be removed in 4.0. Please use `AbstractRealDistribution(RandomGenerator)` instead.

#### AbstractRealDistribution

    protected AbstractRealDistribution(RandomGenerator rng)

Parameters:
  `rng` - Random number generator.
Since:
  3.1

### Method Detail

#### cumulativeProbability

    @Deprecated
    public double cumulativeProbability(double x0,
                                          double x1)
                                 throws NumberIsTooLargeException

Deprecated. As of 3.1 (to be removed in 4.0). Please use `probability(double,double)` instead.
For a random variable `X` whose values are distributed according to this distribution, this method returns `P(x0 < X <= x1)`. The default implementation uses the identity

`P(x0 < X <= x1) = P(X <= x1) - P(X <= x0)`

Specified by:
  `cumulativeProbability` in interface `RealDistribution`
Parameters:
  `x0` - the exclusive lower bound
  `x1` - the inclusive upper bound
Returns:
  the probability that a random variable with this distribution takes a value between `x0` and `x1`, excluding the lower and including the upper endpoint
Throws:
  `NumberIsTooLargeException` - if `x0 > x1`

#### probability

    public double probability(double x0,
                     double x1)

For a random variable `X` whose values are distributed according to this distribution, this method returns `P(x0 < X <= x1)`.

Parameters:
  `x0` - Lower bound (excluded).
  `x1` - Upper bound (included).
Returns:
  the probability that a random variable with this distribution takes a value between `x0` and `x1`, excluding the lower and including the upper endpoint.
Throws:
  `NumberIsTooLargeException` - if `x0 > x1`. The default implementation uses the identity `P(x0 < X <= x1) = P(X <= x1) - P(X <= x0)`
Since:
  3.1

#### inverseCumulativeProbability

    public double inverseCumulativeProbability(double p)
                                        throws OutOfRangeException

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`
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`

#### 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.

Returns:
  the maximum absolute error in inverse cumulative probability estimates

#### reseedRandomGenerator

    public void reseedRandomGenerator(long seed)

Reseed the random generator used to generate samples.

Specified by:
  `reseedRandomGenerator` in interface `RealDistribution`
Parameters:
  `seed` - the new seed

#### 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`
Returns:
  a random value.

#### sample

    public double[] sample(int sampleSize)

Generate a random sample from the distribution. The default implementation generates the sample by calling `sample()` in a loop.

Specified by:
  `sample` in interface `RealDistribution`
Parameters:
  `sampleSize` - the number of random values to generate
Returns:
  an array representing the random sample

#### 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.

Specified by:
  `probability` in interface `RealDistribution`
Parameters:
  `x` - the point at which the PMF is evaluated
Returns:
  zero.
Since:
  3.1