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Due to a stochastic character of the intensities of information flows in high performance information systems, the size of data available for the statistical analysis can be often regarded as random. In the paper general theorem concerning the deficiencies of some estimators and the asymptotic expansions of the distribution function of the statistics based on the sample of random size was proved. Some examples are presented for the cases where the sample size has the negative binomial or discrete Pareto distributions. 

sample of random size, asymptotic expansions, asymptotic deficiency, statistical estimator, risk function, asymptotic relative efficiency.