optimum_interval

Yellin's maximum-gap and optimum-interval methods for frequentist upper limits in the presence of an unknown, non-subtractable background — using only the signal shape, with no background model and no binning.

• Tutorial — from a signal spectrum to an exclusion curve.
• Explanation — the derivation and a reimplement-it-yourself recipe.
• API reference — the public functions and classes.

import numpy as np
from optimum_interval import OptimumIntervalTable

table = OptimumIntervalTable(rng=np.random.default_rng(0))
events = np.sort(np.random.default_rng(1).random(8))   # events in cumulant space
print(table.upper_limit(events, confidence=0.9, n=2000))

Method reference: S. Yellin, "Finding an Upper Limit in the Presence of Unknown Background", Phys. Rev. D66 (2002) 032005, arXiv:physics/0203002.