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Relative error of the estimations of different error characteristics

In the present paper 9 error characteristics are detailedly investigated by Monte Carlo calculations in point of view of the fluctuation of their estimates. In all 9 cases the error characteristic is defined as the minimum value of a modern norm of deviations, just in the same manner as in the classical statistics the σ scatter was defined as the minimum value of the L2-norm. The results are in Table I summarized and in Figs 1–9 presented for five parent distribution types and for five sample sizes: n = 5; 9; 25; 100 and 400; the statistical fluctuation is characterized by the relative semi-intersextile ranges of the minimum norms (N = 200000 repetition number was chosen in the Monte Carlo calculations). On the basis of the values of Table I the uncertainties can be determined with such accuracy which is seldom required in the practice. Because of the fact that ordinarily 15–20 % is accepted as the “error of the error”, in the Table III asymptotic values are also given to give possibility to the simplest: according to Aasympt/√n executed calculations.