Serializable
, RealDistribution
public class CauchyDistribution extends AbstractRealDistribution
DEFAULT_SOLVER_ABSOLUTE_ACCURACY
Constructor | 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.
|
Modifier and Type | Method | 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.
|
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.
|
getSolverAbsoluteAccuracy, logDensity, probability
public CauchyDistribution()
public CauchyDistribution(double median, double scale) throws MathIllegalArgumentException
median
- Median for this distributionscale
- Scale parameter for this distributionMathIllegalArgumentException
- if scale <= 0
public double cumulativeProbability(double x)
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.x
- the point at which the CDF is evaluatedx
public double getMedian()
public double getScale()
public double density(double x)
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.x
- the point at which the PDF is evaluatedx
public double inverseCumulativeProbability(double p) throws MathIllegalArgumentException
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
.RealDistribution.getSupportLowerBound()
for p = 0
,RealDistribution.getSupportUpperBound()
for p = 1
.Double.NEGATIVE_INFINITY
when p == 0
and Double.POSITIVE_INFINITY
when p == 1
.inverseCumulativeProbability
in interface RealDistribution
inverseCumulativeProbability
in class AbstractRealDistribution
p
- the cumulative probabilityp
-quantile of this distribution
(largest 0-quantile for p = 0
)MathIllegalArgumentException
- if p < 0
or p > 1
public double getNumericalMean()
public double getNumericalVariance()
public double getSupportLowerBound()
inverseCumulativeProbability(0)
. In other words, this
method must return
inf {x in R | P(X <= x) > 0}
.
public double getSupportUpperBound()
inverseCumulativeProbability(1)
. In other words, this
method must return
inf {x in R | P(X <= x) = 1}
.
public boolean isSupportConnected()
true
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