Experimental applications · descriptive only
Applying the Weibull model: three experiments
Each experiment applies the same two-sided Weibull fit used in the ledger to a different question. Figures are computed from completed Binance daily candles. They describe model behaviour and are not recommendations.
Experiment 1
Weibull vs Gaussian: tail exceedance test
Walk-forward over the last 180 days for 0 assets: each day both models are fitted on the prior 365 daily returns only, then asked for P(|daily return| > x). Lower Brier is better.
| Move > | n | Observed | Weibull | Gaussian | Brier W | Brier G |
|---|---|---|---|---|---|---|
| ±3% | 1 | 0.00% | 0.00% | 0.00% | 0.0000 | 0.0000 |
| ±5% | 1 | 0.00% | 0.00% | 0.00% | 0.0000 | 0.0000 |
| ±8% | 1 | 0.00% | 0.00% | 0.00% | 0.0000 | 0.0000 |
| ±10% | 1 | 0.00% | 0.00% | 0.00% | 0.0000 | 0.0000 |
Pooled across assets; days are correlated across assets, so n overstates independent evidence. Out-of-sample: no fit saw the day it was scored on.
Experiment 2
Shape-parameter radar (k)
k below 1 indicates heavier tails than exponential; a falling k signals tail thickening. Current fit (last 365 days) against the fit as of 30 days earlier.
| Asset | k down | Δ 30d | k up | Δ 30d |
|---|
Experiment 3
Live corridor stress test (24h)
Position of the live price inside today's locked 24h corridor (0% = floor, 100% = ceiling). Live quotes are display-only; resolution uses the 00:00 UTC daily close.