The membranes of cells, such as those found in heart and nerve tissue, contain structures known as ion channels. The current produced by an ion channel in a cell membrane has been modelled as a finite state-space Markov process. Statistical analysis of ion channels has been largely limited to the case where a single channel is observed, or where the stimulus to the channel is so slight that only one channel at a time is emitting current. In many experiments, however, several channels are producing current simultaneously. Therefore only the superposition of the currents from an unknown number of channels can be observed. A hypothesis test is established which tests whether these channels operate independently and identically. If the null hypothesis is not rejected, confidence intervals for the mean emitting time and mean nonemitting time of individual channels and estimates of the distribution functions of the sojourns in emitting states and nonemitting states are obtained.
"Renewal Theory Properties of Ion Channels." Ann. Statist. 18 (3) 1091 - 1115, September, 1990. https://doi.org/10.1214/aos/1176347741