The modern statistical distribution theory is applied to the development of the overdispersion theory in ionizing-radiation statistics for the first time. The physical nuclear system is treated as a sequence of binomial processes, each depending on a characteristic probability, such as probability of decay, detection, etc. The probabilities fluctuate in the course of a measurement, and the physical reasons for that are discussed. If the average values of the probabilities change from measurement to measurement, which originates from the random Lexis binomial sampling scheme, then the resulting distribution is overdispersed. The generating functions and probability distribution functions are derived, followed by a moment analysis. The Poisson and Gaussian limits are also given. The distribution functions belong to a family of generalized hypergeometric factorial moment distributions by Kemp and Kemp, and can serve as likelihood functions for the statistical estimations. An application to radioactive decay with detection is described and working formulae are given, including a procedure for testing the counting data for overdispersion. More complex experiments in nuclear physics (such as solar neutrino) can be handled by this model, as well as distinguishing between the source and background.
Classical mathematics is a source of ideas used by Computer Science since the very first days. Surprisingly, there is still much to be found. Computer scientists, especially, those in Theoretical Computer Science find inspiring ideas both in old notions and results, and in the 20th century mathematics. The latest decades have brought us evidence that computer people will soon study quantum physics and modern biology just to understand what computers are doing. 2b1af7f3a8