Tail entropy approximations

A three parameter tail entropy approximation (TEA) suitable for reliability and risk analysis is described and illustrated by examples. The TEA is determined directly from sample data. It combines the best features of tail approximation and entropy optimization for structural safety analysis. Estimation of the distributions of basic random variables from sample data is a critical step in the analysis of structural safety and other random phenomena. Standard estimation methods may be simple, but results are sensitive to the necessary but arbitrary assumptions about distribution type. The method of minimum relative entropy is more objective and less sensitive to arbitrary assumptions, but requires optimization procedures and some of the results are mathematically intractable. The TEA method is a tractable and accurate combination, useful when a tail approximation is appropriate.