Calculation of the asymptotic deficiency of some statistical procedures based on samples with random sizes

Statistical regularities of information flows in contemporary communication, computational and other information systems are characterized by the presence of the so-called “heavy tails”. The random character of the intensity of the flow of informative events results in that the available sample size (traditionally, this is the number of observations registered within a certain time interval) is random. The randomness of the sample size cruciall changes the asymptotic properties of the statistical procedures (e.g., estimators). The present paper consists of a number of applications of the deficiency concept, i.e., the number of additional observations required by the less effective procedure and, thereby, provides a basis for deciding whether or not the price is too high. The deficiency was introduced by Hodges and Lehmann in 1970. In the paper, asymptotic deficiencies of statistical procedures based on samples with random sizes are considered. Three examples concerning testing statistical hypotheses, point, and confidence estimation are presented.