Some Conservative and Efficient Sparse-Sample Tail Probability Estimation Methods and Practical Motivation for Them

Engineered systems sometimes involve significant stochastic/random variability of materials, geometry/hardware, failure thresholds, etc. In these systems it is important to appropriately account for related uncertainty in engineering analysis supporting robust/reliable design, safety/risk analysis, decision-making, etc. Typically in engineering situations, aleatory variability can only be sampled very sparsely by physical experimentation and testing, yet there is often a need to estimate percentiles and probabilities associated with tails of unknown frequency distributions from which the few samples come. In this paper we describe motivating circumstances and effective methods for conservative and efficient estimation of tail percentiles and probabilities of magnitudes 10-5 to 10-1 based on very few samples (2 – 20) from a variety of distribution types and shapes. We summarize testing of the methods for conservative and efficient estimation of tail statistics of 16 test distributions including highly non-Normal, highly skewed, and multi-modal distributions, and provide interim insights for the best method(s) to use in various regions of the studied factor space.