public class GeneralizedParetoDistribution extends Object implements UnivariateEVD
| Constructor and Description |
|---|
GeneralizedParetoDistribution()
Create an instance with the default parameter values: location \(\mu=0\), scale \(\sigma=1\),
shape \(\xi=0\).
|
GeneralizedParetoDistribution(double scale,
double shape)
Create an instance with zero location, and the given scale and shape parameters.
|
GeneralizedParetoDistribution(double location,
double scale,
double shape)
Create an instance with the given parameter values.
|
| Modifier and Type | Method and Description |
|---|---|
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
\(\xi <0\).
|
double |
entropy()
Gets the entropy of this distribution.
|
double |
kurtosis()
Gets the excess kurtosis of this distribution.
|
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()
\[
\mu + \frac{\sigma( 2^{\xi} -1)}{\xi}
\]
|
double |
moment(double x)
The moment generating function is the expected value of etX.
|
double |
quantile(double p)
Gets the quantile, the inverse of the cumulative distribution function.
|
double |
skew()
Gets the skewness of this distribution.
|
double |
variance()
\[
\frac{\sigma^2}{(1-\xi)^2(1-2\xi)}
\]
for \(\xi < 1/2\).
|
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 ProbabilityDistributionx - \(x\)public double logDensity(double x)
UnivariateEVDlogDensity in interface UnivariateEVDx - \(x\)public double cdf(double x)
ProbabilityDistributioncdf in interface ProbabilityDistributionx - xpublic double quantile(double p)
ProbabilityDistributionThis may not always exist.F-1(u) = x, such that Pr(X ≤ x) = u
quantile in interface ProbabilityDistributionp - u, a quantilepublic double mean()
mean in interface ProbabilityDistributionpublic double moment(double x)
ProbabilityDistributionE(etX)This may not always exist.
moment in interface ProbabilityDistributionx - tpublic double skew()
ProbabilityDistributionskew in interface ProbabilityDistributionpublic double variance()
variance in interface ProbabilityDistributionpublic double median()
median in interface ProbabilityDistributionpublic double kurtosis()
ProbabilityDistributionkurtosis in interface ProbabilityDistributionpublic double entropy()
ProbabilityDistributionentropy in interface ProbabilityDistributionCopyright © 2010-2020 NM FinTech Ltd.. All Rights Reserved.