  An electron-multiplying charge-coupled device (EMCCD) is often used for
taking images with space telescopes and other devices. Photons hit the pixels
and photo-electrons are created, and these are multiplied via impact ionization
as they travel through the gain register from one gain stage to the next. A
high gain means a high multiplication factor, and this is achieved through a
high voltage difference across a gain stage. If the gain is high enough, the
chance of clock-induced charge production in the gain register increases. The
probability distribution function governing the gain process in the literature
only accounts for charge multiplication if one or more electrons enters the
gain register. I derive from first principles the modified probability
distribution that accounts for clock-induced charge production in the gain
register. I also examine some EMCCD data and show through maximum likelihood
estimation that the data conform better to the modified distribution versus the
usual one in the literature. The use of the modified distribution would in
principle improve the accuracy of signal extraction from a frame.
