Package dev.nm.stat.evt.evd.univariate

Interface UnivariateEVD

All Superinterfaces:

ProbabilityDistribution

All Known Implementing Classes:

FrechetDistribution, GeneralizedEVD, GeneralizedParetoDistribution, GumbelDistribution, MaximaDistribution, MinimaDistribution, OrderStatisticsDistribution, ReversedWeibullDistribution

public interface UnivariateEVD
extends ProbabilityDistribution

Distribution of extreme values (e.g., maxima, minima, or other order statistics).

The extreme value theorem (also the Fisher-Tippett-Gnedenko theorem or the Fisher-Tippett theorem) is a general result in extreme value theory regarding asymptotic distribution of extreme order statistics. The maximum of a sample of IID random variables after proper renormalization converges in distribution to one of 3 possible distributions, the Gumbel distribution, the Fréchet distribution, or the Weibull distribution.

The role of the extremal types theorem for maxima is similar to that of central limit theorem for averages.

See Also:

• Wikipedia: Extreme value theory

Method Summary

Modifier and Type	Method	Description
double	logDensity(double x)	Get the logarithm of the probability density function at \(x\), that is, \(\log(f(x))\).

Methods inherited from interface dev.nm.stat.distribution.univariate.ProbabilityDistribution

cdf, density, entropy, kurtosis, mean, median, moment, quantile, skew, variance

Method Details

logDensity

double logDensity(double x)

Get the logarithm of the probability density function at \(x\), that is, \(\log(f(x))\).

Parameters:

x - \(x\)

Returns:

\(\log(f(x))\)