Second-order distributions: construction, operations, applications

The article considers methods for studying the uncertainties of probabilistic estimates of empirical distribution functions. To this end, a new approach based on the concept of a second-order distribution is proposed. For numerical implementations of operations on second-order distributions, probabilistic extensions of their parametrized representations are used. Examples of using this approach to assess the reliability of technical objects under conditions of small samples are given. Contribution of the authors: the authors contributed equally to this article. The authors declare no conflicts of interests.

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