Centralized inverse-Fano distribution for controlling conversion gain measurement accuracy of detector elements

Statistical theory is applied to derive the centralized inverse-Fano distribution as a model for the probability distribution of the photon transfer conversion gain measurement for detector elements. This distribution is confirmed by experiment, thus supporting the theory and enhancing the credibility of the statistical model used. Analysis of the statistical distance between the derived functions and computationally fast approximate forms is carried out to determine the conditions when such approximations are useful. Theoretical results are then applied to develop algorithms for use in live experiments to calculate appropriate sample sizes for measuring the conversion gain given a user-specified acceptable uncertainty.