org.apache.commons.statistics.distribution

## Class CauchyDistribution

• java.lang.Object
• org.apache.commons.statistics.distribution.CauchyDistribution

• ### Nested classes/interfaces inherited from interface org.apache.commons.statistics.distribution.ContinuousDistribution

ContinuousDistribution.Sampler
• ### Constructor Summary

Constructors
Constructor and Description
CauchyDistribution(double median, double scale)
Creates a distribution.
• ### Method Summary

All Methods
Modifier and Type Method and Description
ContinuousDistribution.Sampler createSampler(org.apache.commons.rng.UniformRandomProvider rng)
Creates a sampler.
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 getMean()
Gets the mean of this distribution.
double getMedian()
Access the median.
double getScale()
Access the scale parameter.
double getSupportLowerBound()
Gets the lower bound of the support.
double getSupportUpperBound()
Gets the upper bound of the support.
double getVariance()
Gets the variance of this distribution.
double inverseCumulativeProbability(double p)
Computes the quantile function of this distribution.
boolean isSupportConnected()
Indicates whether the support is connected, i.e.
static double[] sample(int n, ContinuousDistribution.Sampler sampler)
Utility function for allocating an array and filling it with n samples generated by the given sampler.
• ### 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.statistics.distribution.ContinuousDistribution

logDensity, probability, probability
• ### Constructor Detail

• #### CauchyDistribution

public CauchyDistribution(double median,
double scale)
Creates a distribution.
Parameters:
median - Median for this distribution.
scale - Scale parameter for this distribution.
Throws:
IllegalArgumentException - if scale <= 0.
• ### 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 - 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 - Point at which the PDF is evaluated.
Returns:
the value of the probability density function at x.
• #### inverseCumulativeProbability

public double inverseCumulativeProbability(double p)
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 Returns Double.NEGATIVE_INFINITY when p == 0 and Double.POSITIVE_INFINITY when p == 1.
Specified by:
inverseCumulativeProbability in interface ContinuousDistribution
Parameters:
p - Cumulative probability.
Returns:
the smallest p-quantile of this distribution (largest 0-quantile for p = 0).
• #### getMean

public double getMean()
Gets the mean of this distribution. The mean is always undefined no matter the parameters.
Returns:
mean (always Double.NaN)
• #### getVariance

public double getVariance()
Gets the variance of this distribution. The variance is always undefined no matter the parameters.
Returns:
variance (always Double.NaN)
• #### getSupportLowerBound

public double getSupportLowerBound()
Gets the lower bound of the support. It must return the same value as inverseCumulativeProbability(0), i.e. 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()
Gets the upper bound of the support. It must return the same value as inverseCumulativeProbability(1), i.e. 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)
• #### isSupportConnected

public boolean isSupportConnected()
Indicates 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 static double[] sample(int n,
ContinuousDistribution.Sampler sampler)
Utility function for allocating an array and filling it with n samples generated by the given sampler.
Parameters:
n - Number of samples.
sampler - Sampler.
Returns:
an array of size n.
• #### createSampler

public ContinuousDistribution.Sampler createSampler(org.apache.commons.rng.UniformRandomProvider rng)
Creates a sampler.
Specified by:
createSampler in interface ContinuousDistribution
Parameters:
rng - Generator of uniformly distributed numbers.
Returns:
a sampler that produces random numbers according this distribution.