Class LevyDistribution
java.lang.Object
org.hipparchus.distribution.continuous.AbstractRealDistribution
org.hipparchus.distribution.continuous.LevyDistribution
- All Implemented Interfaces:
Serializable
,RealDistribution
This class implements the
Lévy distribution.
- See Also:
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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
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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
Get the location parameter of the distribution.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()
Get the scale parameter of the distribution.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.double
logDensity
(double x) Returns the natural logarithm of the probability density function (PDF) of this distribution evaluated at the specified pointx
.Methods inherited from class org.hipparchus.distribution.continuous.AbstractRealDistribution
getSolverAbsoluteAccuracy, probability
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Constructor Details
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LevyDistribution
public LevyDistribution(double mu, double c) Build a new instance.- Parameters:
mu
- location parameterc
- scale parameter
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Method Details
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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.From Wikipedia: The probability density function of the Lévy distribution over the domain is
\[ f(x; \mu, c) = \sqrt{\frac{c}{2\pi}} \frac{e^{\frac{-c}{2 (x - \mu)}}}{(x - \mu)^\frac{3}{2}} \]For this distribution,
X
, this method returnsP(X < x)
. Ifx
is less than location parameter μ,Double.NaN
is returned, as in these cases the distribution is not defined.- 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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logDensity
public double logDensity(double x) Returns the natural logarithm of 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. Note that due to the floating point precision and under/overflow issues, this method will for some distributions be more precise and faster than computing the logarithm ofRealDistribution.density(double)
.The default implementation simply computes the logarithm of
density(x)
. See documentation ofdensity(double)
for computation details.- Specified by:
logDensity
in interfaceRealDistribution
- Overrides:
logDensity
in classAbstractRealDistribution
- Parameters:
x
- the point at which the PDF is evaluated- Returns:
- the logarithm of the value of the probability density function at point
x
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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.From Wikipedia: the cumulative distribution function is
f(x; u, c) = erfc (√ (c / 2 (x - u )))
- 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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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
.
- 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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getScale
public double getScale()Get the scale parameter of the distribution.- Returns:
- scale parameter of the distribution
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getLocation
public double getLocation()Get the location parameter of the distribution.- Returns:
- location parameter of the distribution
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getNumericalMean
public double getNumericalMean()Use this method to get the numerical value of the mean of this distribution.- Returns:
- the mean or
Double.NaN
if it is not defined
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getNumericalVariance
public double getNumericalVariance()Use this method to get the numerical value of the variance of this distribution.- Returns:
- the variance (possibly
Double.POSITIVE_INFINITY
as for certain cases inTDistribution
) orDouble.NaN
if it is not defined
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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 returninf {x in R | P(X <= x) > 0}
.- Returns:
- lower bound of the support (might be
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 returninf {x in R | P(X <= x) = 1}
.- Returns:
- upper bound of the support (might be
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.- Returns:
- whether the support is connected or not
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