Struct GpdParameters 

pub struct GpdParameters {
    pub shape: f64,
    pub scale: f64,
    pub threshold: f64,
}

Parameters of the Generalized Pareto Distribution.

The GPD CDF is:

• F(x) = 1 - (1 + ξx/σ)^(-1/ξ) for ξ ≠ 0
• F(x) = 1 - exp(-x/σ) for ξ = 0 (exponential)

The shape parameter ξ (xi) determines tail behavior:

• ξ > 0: heavy-tailed (Pareto-type), infinite higher moments
• ξ = 0: exponential tails (light-tailed)
• ξ < 0: bounded support, finite endpoint at -σ/ξ

Fields

shape: f64

Shape parameter (xi). Controls tail heaviness.

scale: f64

Scale parameter (sigma). Must be positive.

threshold: f64

Threshold above which GPD applies.

Implementations

impl GpdParameters

pub fn new(shape: f64, scale: f64, threshold: f64) -> Self

Create new GPD parameters.

Panics

Panics if scale is not positive.

pub fn quantile(&self, p: f64) -> f64

Compute the quantile (inverse CDF) for probability p.

Returns the value x such that P(X <= x) = p for exceedances.

pub fn survival_probability(&self, x: f64) -> f64

Compute the survival probability P(X > x) for exceedance x above threshold.

pub fn pot_quantile(&self, p: f64, n: usize, nu: usize) -> f64

Estimate the extreme quantile using POT (Peaks Over Threshold).

Given n total observations and nu threshold exceedances, estimates the p-quantile of the original distribution.

Trait Implementations

impl Clone for GpdParameters

fn clone(&self) -> GpdParameters

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Copy for GpdParameters

impl Debug for GpdParameters

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl PartialEq for GpdParameters

fn eq(&self, other: &GpdParameters) -> bool

Tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl StructuralPartialEq for GpdParameters