CauchyDistribution (Apache Commons Math 3.6.1 API)

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

All Implemented Interfaces:

Serializable, RealDistribution
```
public class CauchyDistribution
extends AbstractRealDistribution
```
Implementation of the Cauchy distribution.

Since:

1.1 (changed to concrete class in 3.0)

See Also:
Cauchy distribution (Wikipedia), Cauchy Distribution (MathWorld), Serialized Form

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
  random, randomData, SOLVER_DEFAULT_ABSOLUTE_ACCURACY

Fields
Modifier and Type	Field and Description
`static double`	`DEFAULT_INVERSE_ABSOLUTE_ACCURACY` Default inverse cumulative probability accuracy.

Constructor Summary

Constructors
Constructor and Description
`CauchyDistribution()` Creates a Cauchy distribution with the median equal to zero and scale equal to one.
`CauchyDistribution(double median, double scale)` Creates a Cauchy distribution using the given median and scale.
`CauchyDistribution(double median, double scale, double inverseCumAccuracy)` Creates a Cauchy distribution using the given median and scale.
`CauchyDistribution(RandomGenerator rng, double median, double scale)` Creates a Cauchy distribution.
`CauchyDistribution(RandomGenerator rng, double median, double scale, double inverseCumAccuracy)` Creates a Cauchy distribution.

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`	`getMedian()` Access the median.
`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.
`double`	`getScale()` Access the scale parameter.
`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.
`double`	`inverseCumulativeProbability(double p)` Computes the quantile function of this distribution.
`boolean`	`isSupportConnected()` Use this method to get information about whether the support is connected, i.e.
`boolean`	`isSupportLowerBoundInclusive()` Whether or not the lower bound of support is in the domain of the density function.
`boolean`	`isSupportUpperBoundInclusive()` Whether or not the upper bound of support is in the domain of the density function.

Methods inherited from class org.apache.commons.math3.distribution.AbstractRealDistribution
cumulativeProbability, logDensity, probability, probability, reseedRandomGenerator, sample, 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.
    
    Since:
    
    2.1
    
    See Also:
    Constant Field Values
- Constructor Detail
  - CauchyDistribution
```
public CauchyDistribution()
```
    Creates a Cauchy distribution with the median equal to zero and scale equal to one.
  - CauchyDistribution
```
public CauchyDistribution(double median,
                  double scale)
```
    Creates a Cauchy distribution using the given median and scale.
    Note: this constructor will implicitly create an instance of Well19937c as random generator to be used for sampling only (see AbstractRealDistribution.sample() and AbstractRealDistribution.sample(int)). In case no sampling is needed for the created distribution, it is advised to pass null as random generator via the appropriate constructors to avoid the additional initialisation overhead.
    
    Parameters:
    median - Median for this distribution.
    scale - Scale parameter for this distribution.
  - CauchyDistribution
```
public CauchyDistribution(double median,
                  double scale,
                  double inverseCumAccuracy)
```
    Creates a Cauchy distribution using the given median and scale.
    Note: this constructor will implicitly create an instance of Well19937c as random generator to be used for sampling only (see AbstractRealDistribution.sample() and AbstractRealDistribution.sample(int)). In case no sampling is needed for the created distribution, it is advised to pass null as random generator via the appropriate constructors to avoid the additional initialisation overhead.
    
    Parameters:
    median - Median for this distribution.
    scale - Scale parameter for this distribution.
    inverseCumAccuracy - Maximum absolute error in inverse cumulative probability estimates (defaults to DEFAULT_INVERSE_ABSOLUTE_ACCURACY).
    
    Throws:
    
    NotStrictlyPositiveException - if scale <= 0.
    Since:
    
    2.1
  - CauchyDistribution
```
public CauchyDistribution(RandomGenerator rng,
                  double median,
                  double scale)
```
    Creates a Cauchy distribution.
    
    Parameters:
    rng - Random number generator.
    median - Median for this distribution.
    scale - Scale parameter for this distribution.
    
    Throws:
    
    NotStrictlyPositiveException - if scale <= 0.
    Since:
    
    3.3
  - CauchyDistribution
```
public CauchyDistribution(RandomGenerator rng,
                  double median,
                  double scale,
                  double inverseCumAccuracy)
```
    Creates a Cauchy distribution.
    
    Parameters:
    rng - Random number generator.
    median - Median for this distribution.
    scale - Scale parameter for this distribution.
    inverseCumAccuracy - Maximum absolute error in inverse cumulative probability estimates (defaults to DEFAULT_INVERSE_ABSOLUTE_ACCURACY).
    
    Throws:
    
    NotStrictlyPositiveException - if scale <= 0.
    Since:
    
    3.1
- Method Detail
  - 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
  - getMedian
```
public double getMedian()
```
    Access the median.
    
    Returns:
    the median for this distribution.
  - getScale
```
public double getScale()
```
    Access the scale parameter.
    
    Returns:
    the scale parameter for this distribution.
  - 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
  - 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.
    Returns Double.NEGATIVE_INFINITY when p == 0 and Double.POSITIVE_INFINITY when 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
  - 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. The mean is always undefined no matter the parameters.
    
    Returns:
    mean (always Double.NaN)
  - getNumericalVariance
```
public double getNumericalVariance()
```
    Use this method to get the numerical value of the variance of this distribution. The variance is always undefined no matter the parameters.
    
    Returns:
    variance (always Double.NaN)
  - 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 always negative infinity no matter the parameters.
    
    Returns:
    lower bound of the support (always Double.NEGATIVE_INFINITY)
  - 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 always positive infinity no matter the parameters.
    
    Returns:
    upper bound of the support (always Double.POSITIVE_INFINITY)
  - 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

Class CauchyDistribution

Field Summary

Fields inherited from class org.apache.commons.math3.distribution.AbstractRealDistribution

Constructor Summary

Method Summary

Methods inherited from class org.apache.commons.math3.distribution.AbstractRealDistribution

Methods inherited from class java.lang.Object

Field Detail

DEFAULT_INVERSE_ABSOLUTE_ACCURACY

Constructor Detail

CauchyDistribution

CauchyDistribution

CauchyDistribution

CauchyDistribution

CauchyDistribution

Method Detail

cumulativeProbability

getMedian

getScale

density

inverseCumulativeProbability

getSolverAbsoluteAccuracy

getNumericalMean

getNumericalVariance

getSupportLowerBound

getSupportUpperBound

isSupportLowerBoundInclusive

isSupportUpperBoundInclusive

isSupportConnected