  The steeply falling jet spectrum induces bias on the medium modifications of
jet observables in heavy-ion collisions. To explore this bias, we develop a
novel analytic framework to study the quenched jet spectrum, and its
cumulative. We include many energy-loss-related effects, such as soft and hard
medium induced emissions, broadening, elastic scattering, jet fragmentation,
cone size, coherence effects, etc. We show that, different jet spectrum-based
observables are connected, e.g., the nuclear modification, spectrum shift, and
the quantile procedure. We present the first predictions for the nuclear
modification factor and the quantile procedure with cone size dependence. As an
example, we compare dijet and boson+jet events to unfold the spectrum bias
effects. We improve quark-, and gluon-jet classification using arguments based
on the cumulative. Besides pointing out its flexibility, we apply our framework
with other energy loss models such as the hybrid weak-, strong-coupling.
