What tailspec Measures

the library · tail heaviness

Tail Heaviness

Does the model's distribution reach as far as the observed one?

GEV and GPD shape parameter (ξ)

Extreme-value fits per grid cell, from block maxima and peaks-over-threshold. Too small a ξ is a tail that thins out too fast.

Return level curves

The 1-in-N event each distribution implies, compared as N grows.

Q-Q tail plots

Forecast quantiles against reference quantiles in the top of the distribution.

Percentile bias maps

Where the P99 and P99.9 fields are biased, and by how much.

the library · tail calibration

Tail Calibration

When the model says a 1-in-100 event, is it 1-in-100?

Occurrence ratio

Exceedances observed compared with exceedances forecast, per threshold (Allen et al. 2024).

Severity ratio

Given an exceedance, how far past the threshold the outcome went, compared with the forecast.

Excess distribution and PIT diagnostics

Calibration of the conditional distribution past the threshold, not only of its frequency.

the library · records

Record-Breaking Events

Conditioned on the forecast rather than the outcome, so the forecaster's dilemma does not apply.

Record-conditioned error

Forecast error on the events the model itself flags as record-breaking (Zhang et al. 2026).

Record detection skill

Precision, recall and Brier skill for record-breaking occurrence.

the library · probabilistic skill

Probabilistic Skill in the Tail

Proper scores, weighted toward the part of the distribution that matters.

Threshold-weighted CRPS

CRPS with its weight on the tail, the standard remedy for outcome-conditioned verification (Gneiting & Ranjan 2011).

Brier skill at extreme percentiles

Exceedance forecasts scored against climatology at P95 and beyond.

Relative economic value

Forecast value across the full range of cost-loss ratios.

Spread-skill and rank histograms, conditioned on extremes

Whether the ensemble's dispersion matches its error where the outcomes are large.

the library · spatial structure

Spatial Structure

Does the model place extremes with the observed spatial coherence, at the resolution it claims?

Tail dependence χ(u, h) and the F-madogram

How the probability of joint extremeness decays with distance, compared with the reference.

Kinetic-energy and temperature spectra

Spectral power by wavenumber, and the effective resolution it implies.

the library · physical consistency

Physical Consistency

Are mass, moisture and energy conserved over a rollout?

Budget drift and residuals

Global mass, moisture and energy accounting across lead time.

Per-member budget scatter

How widely ensemble members disagree on budgets a physics model closes identically.

the library · decision value

Decision Value

What a decision made with the forecast is worth, settled against what happened.

Backtested delivery desks

A day-ahead wind-power book and a four-city temperature quote game, run with real settlement rules and paired bootstrap inference (the In practice page).

Pricing translations

Excess-of-loss layer mispricing and HDD/CDD contract value implied by each model's tail.

the library · design

Two Choices the Case Files Explain

Rarity is measured by return period and by record-breaking events, never by a percentile band conditioned on the observed outcome. Conditioning on the outcome discredits skilful forecasts (Lerch et al. 2017), and the location case file shows the failure mode in a published benchmark. And where a number has to matter, it is settled in money on a backtested book, because a symmetric error metric cannot express an asymmetric cost.