On dead-time corrections for estimating rates

This paper extends analysis given by Larsen and Kostinski (Meas. Sci. Technol. 20 (2009) 095101) for the measurement of the rate of a Poisson process using a counter with dead time. It is shown that when there is dead time after each event, and not merely after each observation of an event, there are two rates that are consistent with the result of any measurement. In this case, extra information is needed if the true rate, λ, is to be recovered unambiguously. Explicit confidence intervals for λ are given for the two types of dead time in the practical situation where the period of observation is finite. The result that two true rates correspond to any rate obtained with the second form of dead time holds with many other processes and with counters in which the dead time is a random variable