public class GeneralizedEVD extends Object implements UnivariateEVD
evd::dgev
, evd::pgev
, evd::qgev
, evd::mtransform
.Constructor and Description |
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GeneralizedEVD()
Create an instance of generalized extreme value distribution with the default parameter
values: location \(\mu=0\), scale \(\sigma=1\), shape \(\xi=0\).
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GeneralizedEVD(double location,
double scale,
double shape)
Create an instance of generalized extreme value distribution with the given parameters.
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Modifier and Type | Method and Description |
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double |
cdf(double x)
Gets the cumulative probability F(x) = Pr(X ≤ x).
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double |
density(double x)
The density function, which, if exists, is the derivative of F.
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double |
entropy()
Gets the entropy of this distribution.
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double |
getLocation()
Get the location parameter.
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double |
getScale()
Get the scale parameter.
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double |
getShape()
Get the shape parameter.
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double |
kurtosis()
Gets the excess kurtosis of this distribution.
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double |
logDensity(double x)
Get the logarithm of the probability density function at \(x\), that is, \(\log(f(x))\).
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double |
marginalInverseTransform(double x)
Inverse of marginal transform.
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double |
marginalTransform(double x)
Transform to exponential margins under the GEV model.
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double |
mean()
Gets the mean of this distribution.
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double |
median()
Gets the median of this distribution.
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double |
moment(double x)
The moment generating function is the expected value of etX.
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double |
quantile(double p)
Gets the quantile, the inverse of the cumulative distribution function.
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double |
skew()
Gets the skewness of this distribution.
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double |
variance()
Gets the variance of this distribution.
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public GeneralizedEVD()
public GeneralizedEVD(double location, double scale, double shape)
location
- the location parameter \(\mu\)scale
- the scale parameter \(\sigma > 0\)shape
- the shape parameter \(\xi\)public double getLocation()
public double getScale()
public double getShape()
public double marginalTransform(double x)
x
- \(x\)public double marginalInverseTransform(double x)
x
- \(x\)public double cdf(double x)
cdf
in interface ProbabilityDistribution
x
- \(x\)public double density(double x)
f(x) = dF(X) / dxThis may not always exist. For the discrete cases, this is the probability mass function. It gives the probability that a discrete random variable is exactly equal to some value. The probability density function of GEV distribution is \[ f(x;\mu,\sigma,\xi) = \frac{1}{\sigma}\left[1+\xi\left(\frac{x-\mu}{\sigma}\right)\right]^{(-1/\xi)-1} \exp\left\{-\left[1+\xi\left(\frac{x-\mu}{\sigma}\right)\right]^{-1/\xi}\right\} \] for \(1+\xi(x-\mu)/\sigma>0\).
density
in interface ProbabilityDistribution
x
- \(x\)public double logDensity(double x)
UnivariateEVD
logDensity
in interface UnivariateEVD
x
- \(x\)public double quantile(double p)
ProbabilityDistribution
This may not always exist.F-1(u) = x, such that Pr(X ≤ x) = u
quantile
in interface ProbabilityDistribution
p
- u
, a quantilepublic double mean()
ProbabilityDistribution
mean
in interface ProbabilityDistribution
public double moment(double x)
ProbabilityDistribution
E(etX)This may not always exist.
moment
in interface ProbabilityDistribution
x
- tpublic double skew()
ProbabilityDistribution
skew
in interface ProbabilityDistribution
public double variance()
ProbabilityDistribution
variance
in interface ProbabilityDistribution
public double median()
ProbabilityDistribution
median
in interface ProbabilityDistribution
public double kurtosis()
ProbabilityDistribution
kurtosis
in interface ProbabilityDistribution
public double entropy()
ProbabilityDistribution
entropy
in interface ProbabilityDistribution
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