public class GeneralizedParetoDistribution extends Object implements UnivariateEVD
Constructor and Description |
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GeneralizedParetoDistribution()
Create an instance with the default parameter values: location \(\mu=0\), scale \(\sigma=1\),
shape \(\xi=0\).
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GeneralizedParetoDistribution(double scale,
double shape)
Create an instance with zero location, and the given scale and shape parameters.
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GeneralizedParetoDistribution(double location,
double scale,
double shape)
Create an instance with the given parameter values.
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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).
|
double |
density(double x)
The probability density function
\[
f(x; \mu,\sigma,\xi) =
\begin{cases}
\frac{1}{\sigma}\left(1+ \frac{\xi (x-\mu)}{\sigma}\right)^{\left(-\frac{1}{\xi} - 1\right)}
& \text{for} \; \xi \neq 0, \\
\frac{1}{\sigma}\exp \left(-\frac{x-\mu}{\sigma}\right) & \text{for} \; \xi = 0
\end{cases}
\]
for \(x \ge \mu\) when \(\xi \ge 0\), and \(\mu \le x \le \mu - \sigma /\xi\) when
\(\xi <0\).
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double |
entropy()
Gets the entropy of this distribution.
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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, \(\log(f(x))\).
|
double |
mean()
\[
\mu + \frac{\sigma}{1-\xi}
\]
for \(\xi < 1\).
|
double |
median()
\[
\mu + \frac{\sigma( 2^{\xi} -1)}{\xi}
\]
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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.
|
double |
skew()
Gets the skewness of this distribution.
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double |
variance()
\[
\frac{\sigma^2}{(1-\xi)^2(1-2\xi)}
\]
for \(\xi < 1/2\).
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public GeneralizedParetoDistribution()
public GeneralizedParetoDistribution(double scale, double shape)
scale
- the scale parameter \(\sigma\)shape
- the shape parameter \(\xi\)public GeneralizedParetoDistribution(double location, double scale, double shape)
location
- the location parameter \(\mu\)scale
- the scale parameter \(\sigma\)shape
- the shape parameter \(\xi\)public double density(double x)
density
in interface ProbabilityDistribution
x
- \(x\)public double logDensity(double x)
UnivariateEVD
logDensity
in interface UnivariateEVD
x
- \(x\)public double cdf(double x)
ProbabilityDistribution
cdf
in interface ProbabilityDistribution
x
- xpublic 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()
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()
variance
in interface ProbabilityDistribution
public double median()
median
in interface ProbabilityDistribution
public double kurtosis()
ProbabilityDistribution
kurtosis
in interface ProbabilityDistribution
public double entropy()
ProbabilityDistribution
entropy
in interface ProbabilityDistribution
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