Radioactivity. Case: Rare events

The paper discusses further development of the approach published in Comp. Phys. Comm. vol. 185(2014), 933–938 (2014). Low statistics means a little of information about the object of interest so that a more or less exact parameter estimation and reliable statistical tests can be only a matter of chance, especially in the case of the exponential distribution which is more intolerant to small samples (1–4 events) than the majority of other important distributions. Therefore, the problem of optimization of the statistical analysis is especially actual for the exponentially distributed data and the paper suggests, for both the parameter (mean) estimation and the statistical tests, a concept of a confidence interval, based on the order statistics, which, on the one hand, provides its clear and natural interpretation, and, on the other hand, is an optimum compromise between the criteria: “the shortest interval length”—“the largest size of the probability.”