public class LevyDistribution extends AbstractRealDistribution
random, randomData, SOLVER_DEFAULT_ABSOLUTE_ACCURACY| Constructor and Description | 
|---|
| LevyDistribution(double mu,
                double c)Build a new instance. | 
| LevyDistribution(RandomGenerator rng,
                double mu,
                double c)Creates a LevyDistribution. | 
| Modifier and Type | Method and Description | 
|---|---|
| double | cumulativeProbability(double x)For a random variable  Xwhose 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 point  x. | 
| double | getLocation()Get the location parameter of the distribution. | 
| 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()Get the scale parameter of the distribution. | 
| 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. | 
| boolean | isSupportLowerBoundInclusive()Whether or not the lower bound of support is in the domain of the density
 function. | 
| boolean | isSupportUpperBoundInclusive()Whether or not the upper bound of support is in the domain of the density
 function. | 
| double | logDensity(double x)Returns the natural logarithm of the probability density function (PDF) of this distribution
 evaluated at the specified point  x. | 
cumulativeProbability, getSolverAbsoluteAccuracy, probability, probability, reseedRandomGenerator, sample, samplepublic LevyDistribution(double mu,
                double c)
 Note: this constructor will implicitly create an instance of
 Well19937c as random generator to be used for sampling only (see
 AbstractRealDistribution.sample() and AbstractRealDistribution.sample(int)). In case no sampling is
 needed for the created distribution, it is advised to pass null
 as random generator via the appropriate constructors to avoid the
 additional initialisation overhead.
mu - location parameterc - scale parameterpublic LevyDistribution(RandomGenerator rng, double mu, double c)
rng - random generator to be used for samplingmu - locationc - scale parameterpublic 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.
 From Wikipedia: The probability density function of the Lévy distribution over the domain is
f(x; μ, c) = √(c / 2π) * e-c / 2 (x - μ) / (x - μ)3/2
 For this distribution, X, this method returns P(X < x).
 If x is less than location parameter μ, Double.NaN is
 returned, as in these cases the distribution is not defined.
 
x - the point at which the PDF is evaluatedxpublic double logDensity(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. 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 of
 RealDistribution.density(double). The default implementation simply computes the logarithm of
 density(x).
 See documentation of density(double) for computation details.logDensity in class AbstractRealDistributionx - the point at which the PDF is evaluatedxpublic 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.
 From Wikipedia: the cumulative distribution function is
f(x; u, c) = erfc (√ (c / 2 (x - u )))
x - the point at which the CDF is evaluatedxpublic double inverseCumulativeProbability(double p)
                                    throws OutOfRangeException
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.inverseCumulativeProbability in interface RealDistributioninverseCumulativeProbability in class AbstractRealDistributionp - the cumulative probabilityp-quantile of this distribution
 (largest 0-quantile for p = 0)OutOfRangeException - if p < 0 or p > 1public double getScale()
public double getLocation()
public double getNumericalMean()
Double.NaN if it is not definedpublic double getNumericalVariance()
Double.POSITIVE_INFINITY as
 for certain cases in TDistribution) or Double.NaN if it
 is not definedpublic double getSupportLowerBound()
inverseCumulativeProbability(0). In other words, this
 method must return
 inf {x in R | P(X <= x) > 0}.
Double.NEGATIVE_INFINITY)public double getSupportUpperBound()
inverseCumulativeProbability(1). In other words, this
 method must return
 inf {x in R | P(X <= x) = 1}.
Double.POSITIVE_INFINITY)public boolean isSupportLowerBoundInclusive()
getSupporLowerBound() is finite and
 density(getSupportLowerBound()) returns a non-NaN, non-infinite
 value.public boolean isSupportUpperBoundInclusive()
getSupportUpperBound() is finite and
 density(getSupportUpperBound()) returns a non-NaN, non-infinite
 value.public boolean isSupportConnected()
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