Statistics of electron-multiplying charge-coupled devices

EMCCDs are efficient imaging devices for low surface brightness UV astronomy. The large amplification allows photon counting, the detection of events versus non-events. This paper provides the statistics of the observation process, the photon-counting process, the amplification, process, and the compression. The expression for the signal-to-noise of photon counting is written in terms of the polygamma function. The optimal exposure time is a function of the clock-induced charge. The exact distribution of amplification process is a simple-to-compute powered matrix. The optimal cutoff for comparing to the read noise is close to a strong function of the read noise and a weak function of the electron-multiplying gain and photon rate. A formula gives the expected compression rate.