Non-Parametric Lower Confidence Bounds for the Fifth Percentile - En 14358 in Comparison to a Fully Non-Parametric Approach

Abstract

In Europe, fifth percentile values are required for the calculation of characteristic values of strength and density. The European standard EN 14358:2016 defined three ways to calculate a 75% lower confidence bound (LCB) for such fifth percentile values, based either on a lognormal parametric approach, on a normal parametric approach or on a non-parametric approach. Using simulated data with different sample sizes and with different underlying distributions, this paper studied the effects of using each of the three approaches of EN 14358. As the third approach in EN 14358 did not seem to be fully non-parametric, the simulation study included, as a fourth approach, a fully non-parametric calculation of the LCB for the fifth percentile. The simulation study confirmed that both non-parametric approaches led to acceptable results for some important distributions, although the non-parametric approach defined in EN 14358 seemed to be more conservative especially for data with a non-normal distribution. The study also confirmed that the use of an incorrect parametric assumption can lead to systematically misleading LCB values for the fifth percentile. The authors recommend replacing the non-parametric approach currently defined in EN 14358 by a fully non-parametric approach. This approach can easily be implemented in a standard.