Class CauchyDistribution
java.lang.Object
org.hipparchus.distribution.continuous.AbstractRealDistribution
org.hipparchus.distribution.continuous.CauchyDistribution
- All Implemented Interfaces:
Serializable
,RealDistribution
Implementation of the Cauchy distribution.
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Field Summary
Fields inherited from class org.hipparchus.distribution.continuous.AbstractRealDistribution
DEFAULT_SOLVER_ABSOLUTE_ACCURACY
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Constructor Summary
ConstructorDescriptionCreates a Cauchy distribution with the median equal to zero and scale equal to one.CauchyDistribution
(double median, double scale) Creates a Cauchy distribution. -
Method Summary
Modifier and TypeMethodDescriptiondouble
cumulativeProbability
(double x) For a random variableX
whose values are distributed according to this distribution, this method returnsP(X <= x)
.double
density
(double x) Returns the probability density function (PDF) of this distribution evaluated at the specified pointx
.double
Access the median.double
Use this method to get the numerical value of the mean of this distribution.double
Use this method to get the numerical value of the variance of this distribution.double
getScale()
Access the scale parameter.double
Access the lower bound of the support.double
Access the upper bound of the support.double
inverseCumulativeProbability
(double p) Computes the quantile function of this distribution.boolean
Use this method to get information about whether the support is connected, i.e.Methods inherited from class org.hipparchus.distribution.continuous.AbstractRealDistribution
getSolverAbsoluteAccuracy, logDensity, probability
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Constructor Details
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CauchyDistribution
public CauchyDistribution()Creates a Cauchy distribution with the median equal to zero and scale equal to one. -
CauchyDistribution
Creates a Cauchy distribution.- Parameters:
median
- Median for this distributionscale
- Scale parameter for this distribution- Throws:
MathIllegalArgumentException
- ifscale <= 0
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Method Details
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cumulativeProbability
public double cumulativeProbability(double x) For a random variableX
whose values are distributed according to this distribution, this method returnsP(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
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getMedian
public double getMedian()Access the median.- Returns:
- the median for this distribution.
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getScale
public double getScale()Access the scale parameter.- Returns:
- the scale parameter for this distribution.
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density
public double density(double x) Returns the probability density function (PDF) of this distribution evaluated at the specified pointx
. In general, the PDF is the derivative of theCDF
. If the derivative does not exist atx
, 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
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inverseCumulativeProbability
Computes the quantile function of this distribution. For a random variableX
distributed according to this distribution, the returned value isinf{x in R | P(X<=x) >= p}
for0 < p <= 1
,inf{x in R | P(X<=x) > 0}
forp = 0
.
RealDistribution.getSupportLowerBound()
forp = 0
,RealDistribution.getSupportUpperBound()
forp = 1
.
Double.NEGATIVE_INFINITY
whenp == 0
andDouble.POSITIVE_INFINITY
whenp == 1
.- Specified by:
inverseCumulativeProbability
in interfaceRealDistribution
- Overrides:
inverseCumulativeProbability
in classAbstractRealDistribution
- Parameters:
p
- the cumulative probability- Returns:
- the smallest
p
-quantile of this distribution (largest 0-quantile forp = 0
) - Throws:
MathIllegalArgumentException
- ifp < 0
orp > 1
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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)
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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)
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getSupportLowerBound
public double getSupportLowerBound()Access the lower bound of the support. This method must return the same value asinverseCumulativeProbability(0)
. In other words, this method must return
The lower bound of the support is always negative infinity no matter the parameters.inf {x in R | P(X <= x) > 0}
.- Returns:
- lower bound of the support (always Double.NEGATIVE_INFINITY)
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getSupportUpperBound
public double getSupportUpperBound()Access the upper bound of the support. This method must return the same value asinverseCumulativeProbability(1)
. In other words, this method must return
The upper bound of the support is always positive infinity no matter the parameters.inf {x in R | P(X <= x) = 1}
.- Returns:
- upper bound of the support (always Double.POSITIVE_INFINITY)
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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
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