Some algebra and statistics on isolated noise events

Noise indices related to isolated emerging noise events are calculated on variable finite durations ΔTev, as opposed to instantaneous levels or indices on constant conventional periods ΔT (1 h, 24 h, ...). Here they are defined by TEL (transit exposure levels) or LeqΔTev on every ΔTev. There are classical formulas to pass from many TELi to the Leq on a longer period including many events. When TELi are supposed equal to TEL one gets classicaly LeqΔT = TEL + 10 log n + K, (CNR, NEF for instance). In algebra, the approach develops some algebraic relations and conditions between total duration ΔT, the global part of all ΔTev,i and their number n, in a way that TEL is clearly emerging from noise level without the isolated events. It is a manner to find a general result like “events kill events,” say that too many events render not emerging any new one. One finds the same with a statistical approach and other appropriate technics (quantiles for instance). And coming on with probabilistic tools, the Bêta distribution renders possible some characterisation of the graphical look of the time evolution of noise level during ΔTev. This work has partly been done with V. Catto of Lyon 1 University.