Class CauchyDistribution

java.lang.Object

org.episteme.core.mathematics.statistics.ContinuousDistribution

org.episteme.core.mathematics.statistics.distributions.CauchyDistribution

All Implemented Interfaces:

Function<Real,Real>, ContinuousFunction<Real,Real>, Function<Real,Real>, Relation<Real,Real>, ProbabilityDistribution

public class CauchyDistribution
extends ContinuousDistribution

Cauchy distribution (also called Lorentz distribution). PDF: f(x) = 1/(πγ[1 + ((x-x₀)/γ)²])

Since:

1.0

Author:

Silvere Martin-Michiellot, Gemini AI (Google DeepMind)

Constructor Summary

Constructors

Constructor	Description
CauchyDistribution()
CauchyDistribution(Real location, Real scale)

Method Summary

Modifier and Type	Method	Description
Real	density(Real x)	Probability density function (PDF) or probability mass function (PMF). f(x) = dP/dx for continuous, P(X = x) for discrete.
Real	mean()	Returns the mean (expected value) of this distribution.
String	toString()
Real	variance()	Returns the variance of this distribution.

Methods inherited from class ContinuousDistribution

cdf, isDiscrete, quantile, sample

Methods inherited from class Object

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

Methods inherited from interface ContinuousFunction

isContinuous

Methods inherited from interface Function

compose

Methods inherited from interface Function

andThen, apply, compose, contains, evaluate, getBackend, isDifferentiable, setBackend

Methods inherited from interface ProbabilityDistribution

evaluate, standardDeviation

Methods inherited from interface Relation

getCodomain, getDomain

Constructor Details

CauchyDistribution

public CauchyDistribution()

CauchyDistribution

public CauchyDistribution(Real location,
 Real scale)

Method Details

density

public Real density(Real x)

Description copied from interface: ProbabilityDistribution

Probability density function (PDF) or probability mass function (PMF). f(x) = dP/dx for continuous, P(X = x) for discrete.

Parameters:

x - the value to evaluate density at

Returns:

the probability density or mass

mean

public Real mean()

Description copied from interface: ProbabilityDistribution

Returns the mean (expected value) of this distribution.

Returns:

the mean

variance

public Real variance()

Description copied from interface: ProbabilityDistribution

Returns the variance of this distribution.

Returns:

the variance

toString

public String toString()

Overrides:

toString in class Object