kstats-distributions/org.oremif.kstats.distributions/GumbelDistribution

GumbelDistribution

class GumbelDistribution(val mu: Double = 0.0, val beta: Double = 1.0) : ContinuousDistribution(source)

The Gumbel distribution (extreme value type I, right-skewed), defined by its location mu and scale beta parameters.

The Gumbel distribution models the distribution of the maximum of a number of samples of various distributions. It is widely used in hydrology (flood analysis), meteorology (extreme weather events), and reliability engineering (failure analysis). Unlike symmetric distributions, the Gumbel has a longer right tail, reflecting the tendency for extreme maxima to be farther from the center than extreme minima.

This implementation corresponds to scipy.stats.gumbel_r (right-skewed Gumbel).

Example:

val dist = GumbelDistribution(mu = 0.0, beta = 1.0)
dist.pdf(0.0)      // 0.3679... (peak density at the mode)
dist.cdf(0.0)      // 0.3679...
dist.quantile(0.5) // 0.3665... (median)
dist.mean           // 0.5772... (Euler-Mascheroni constant)

Constructors

GumbelDistribution

constructor(mu: Double = 0.0, beta: Double = 1.0)

Types

object Companion

Properties

val beta: Double

the scale parameter (spread) of the distribution. Must be positive. Defaults to 1.0.

open override val entropy: Double

The Shannon entropy of this distribution in nats, equal to ln(beta) + 1 + gamma.

open override val kurtosis: Double

The excess kurtosis of this distribution, always 12/5 = 2.4.

open override val mean: Double

The mean of this distribution, equal to mu + beta * gamma (Euler-Mascheroni constant).

the location parameter (mode) of the distribution. Defaults to 0.0.

open override val skewness: Double

The skewness of this distribution, equal to 12 * sqrt(6) * zeta(3) / pi^3, approximately 1.1395.

standardDeviation

open override val standardDeviation: Double

The standard deviation of this distribution, equal to pi * beta / sqrt(6).

open override val variance: Double

The variance of this distribution, equal to (pi * beta)^2 / 6.

Functions

open override fun cdf(x: Double): Double

Returns the cumulative distribution function value at x for this Gumbel distribution.

open override fun logPdf(x: Double): Double

Returns the natural logarithm of the probability density at x for this Gumbel distribution.

open override fun pdf(x: Double): Double

Returns the probability density at x for this Gumbel distribution.

open override fun quantile(p: Double): Double

Returns the quantile (inverse CDF) for the given probability p.

open override fun sample(random: Random): Double

Draws a single random value from this Gumbel distribution using inverse CDF sampling.

open override fun sf(x: Double): Double

Returns the survival function value at x for this Gumbel distribution.