Struct PotTail 

pub struct PotTail { /* private fields */ }

A peaks-over-threshold tail: draws above threshold modelled by a GPD.

P(X > x) = p_u · S_GPD(x - u) for x >= u, where p_u is the share of draws above the threshold. VaR and TVaR at levels p >= 1 - p_u come from the GPD, so they extend smoothly past the largest draw.

use prospicio_core::StreamRng;
use prospicio_prob::{Distribution, Lognormal, Sampled, evt::PotTail};

let d = Lognormal::new(0.0, 1.0).unwrap();
let s = Sampled::new(d.sample(&mut StreamRng::new(3, 0), 100_000)).unwrap();
let tail = PotTail::fit(&s, 0.95).unwrap();
// The 99.9% quantile of LN(0, 1) is 21.98.
let q = tail.var(0.999).unwrap();
assert!((q / 21.98 - 1.0).abs() < 0.05, "{q}");

Implementations

impl PotTail

pub fn fit(draws: &impl Empirical, level: f64) -> Result<Self>

Fits a GPD to the draws above the empirical level quantile of draws (for example 0.95 for the top 5%).

pub fn new(threshold: f64, p_exceed: f64, gpd: Gpd) -> Result<Self>

A tail from known parts; gpd models the exceedances, so its location must be 0.

pub fn threshold(&self) -> f64

pub fn p_exceed(&self) -> f64

Share of draws above the threshold, p_u.

pub fn gpd(&self) -> &Gpd

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

P(X > x) for x >= threshold.

pub fn var(&self, p: f64) -> Result<f64>

VaR at p, for p >= 1 - p_exceed: u + β ((p_u / (1 - p))^ξ - 1) / ξ.

pub fn tvar(&self, p: f64) -> Result<f64>

TVaR at p, for p >= 1 - p_exceed and ξ < 1: (VaR + β - ξ u) / (1 - ξ), the GPD’s mean excess added to the VaR.

Trait Implementations

impl Clone for PotTail

fn clone(&self) -> PotTail

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for PotTail

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

Formats the value using the given formatter.

impl PartialEq for PotTail

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

Equality operator ==.

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

Inequality operator !=.

impl StructuralPartialEq for PotTail