org.apache.commons.math.distribution

## Class CauchyDistributionImpl

• ### Field Summary

Fields
Modifier and Type Field and Description
`static double` `DEFAULT_INVERSE_ABSOLUTE_ACCURACY`
Default inverse cumulative probability accuracy
• ### Constructor Summary

Constructors
Constructor and Description
`CauchyDistributionImpl()`
Creates cauchy distribution with the medain equal to zero and scale equal to one.
```CauchyDistributionImpl(double median, double s)```
Create a cauchy distribution using the given median and scale.
```CauchyDistributionImpl(double median, double s, double inverseCumAccuracy)```
Create a cauchy distribution using the given median and scale.
• ### Method Summary

All Methods
Modifier and Type Method and Description
`double` `cumulativeProbability(double x)`
For this distribution, X, this method returns P(X < `x`).
`double` `density(double x)`
Returns the probability density for a particular point.
`double` `getMedian()`
Access the median.
`double` `getNumericalMean()`
Returns the mean.
`double` `getNumericalVariance()`
Returns the variance.
`double` `getScale()`
Access the scale parameter.
`double` `getSupportLowerBound()`
Returns the lower bound of the support for this distribution.
`double` `getSupportUpperBound()`
Returns the upper bound of the support for this distribution.
`double` `inverseCumulativeProbability(double p)`
For this distribution, X, this method returns the critical point x, such that P(X < x) = `p`.
`void` `setMedian(double median)`
Deprecated.
as of 2.1 (class will become immutable in 3.0)
`void` `setScale(double s)`
Deprecated.
as of 2.1 (class will become immutable in 3.0)
• ### Methods inherited from class org.apache.commons.math.distribution.AbstractContinuousDistribution

`reseedRandomGenerator, sample, sample`
• ### Methods inherited from class org.apache.commons.math.distribution.AbstractDistribution

`cumulativeProbability`
• ### Methods inherited from class java.lang.Object

`equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait`
• ### Methods inherited from interface org.apache.commons.math.distribution.Distribution

`cumulativeProbability`
• ### Field Detail

• #### DEFAULT_INVERSE_ABSOLUTE_ACCURACY

`public static final double DEFAULT_INVERSE_ABSOLUTE_ACCURACY`
Default inverse cumulative probability accuracy
Since:
2.1
Constant Field Values
• ### Constructor Detail

• #### CauchyDistributionImpl

`public CauchyDistributionImpl()`
Creates cauchy distribution with the medain equal to zero and scale equal to one.
• #### CauchyDistributionImpl

```public CauchyDistributionImpl(double median,
double s)```
Create a cauchy distribution using the given median and scale.
Parameters:
`median` - median for this distribution
`s` - scale parameter for this distribution
• #### CauchyDistributionImpl

```public CauchyDistributionImpl(double median,
double s,
double inverseCumAccuracy)```
Create a cauchy distribution using the given median and scale.
Parameters:
`median` - median for this distribution
`s` - scale parameter for this distribution
`inverseCumAccuracy` - the maximum absolute error in inverse cumulative probability estimates (defaults to `DEFAULT_INVERSE_ABSOLUTE_ACCURACY`)
Since:
2.1
• ### Method Detail

• #### cumulativeProbability

`public double cumulativeProbability(double x)`
For this distribution, X, this method returns P(X < `x`).
Specified by:
`cumulativeProbability` in interface `Distribution`
Parameters:
`x` - the value at which the CDF is evaluated.
Returns:
CDF evaluated at `x`.
• #### getMedian

`public double getMedian()`
Access the median.
Specified by:
`getMedian` in interface `CauchyDistribution`
Returns:
median for this distribution
• #### getScale

`public double getScale()`
Access the scale parameter.
Specified by:
`getScale` in interface `CauchyDistribution`
Returns:
scale parameter for this distribution
• #### density

`public double density(double x)`
Returns the probability density for a particular point.
Overrides:
`density` in class `AbstractContinuousDistribution`
Parameters:
`x` - The point at which the density should be computed.
Returns:
The pdf at point x.
Since:
2.1
• #### inverseCumulativeProbability

`public double inverseCumulativeProbability(double p)`
For this distribution, X, this method returns the critical point x, such that P(X < x) = `p`.

Returns `Double.NEGATIVE_INFINITY` for p=0 and `Double.POSITIVE_INFINITY` for p=1.

Specified by:
`inverseCumulativeProbability` in interface `ContinuousDistribution`
Overrides:
`inverseCumulativeProbability` in class `AbstractContinuousDistribution`
Parameters:
`p` - the desired probability
Returns:
x, such that P(X < x) = `p`
Throws:
`java.lang.IllegalArgumentException` - if `p` is not a valid probability.
• #### setMedian

```@Deprecated
public void setMedian(double median)```
Deprecated. as of 2.1 (class will become immutable in 3.0)
Modify the median.
Specified by:
`setMedian` in interface `CauchyDistribution`
Parameters:
`median` - for this distribution
• #### setScale

```@Deprecated
public void setScale(double s)```
Deprecated. as of 2.1 (class will become immutable in 3.0)
Modify the scale parameter.
Specified by:
`setScale` in interface `CauchyDistribution`
Parameters:
`s` - scale parameter for this distribution
Throws:
`java.lang.IllegalArgumentException` - if `sd` is not positive.
• #### getSupportLowerBound

`public double getSupportLowerBound()`
Returns the lower bound of the support for this distribution. The lower bound of the support of the Cauchy distribution is always negative infinity, regardless of the parameters.
Returns:
lower bound of the support (always Double.NEGATIVE_INFINITY)
Since:
2.2
• #### getSupportUpperBound

`public double getSupportUpperBound()`
Returns the upper bound of the support for this distribution. The upper bound of the support of the Cauchy distribution is always positive infinity, regardless of the parameters.
Returns:
upper bound of the support (always Double.POSITIVE_INFINITY)
Since:
2.2
• #### getNumericalMean

`public double getNumericalMean()`
Returns the mean. The mean is always undefined, regardless of the parameters.
Returns:
mean (always Double.NaN)
Since:
2.2
• #### getNumericalVariance

`public double getNumericalVariance()`
Returns the variance. The variance is always undefined, regardless of the parameters.
Returns:
variance (always Double.NaN)
Since:
2.2