A Flexible Distribution Based on L-Moments and Its Application in Structural Reliability

Abstract The distribution information of random variables is essential for reliability engineering analysis. Distribution characteristics are generally described by traditional central moments (C-moments). However, C-moments may not be accurate, especially when the sample size of the data is small. Under these circumstances, linear moments (L-moments) are increasingly used to characterize random variables as they are less influenced by outliers and are more stable than C-moments. In this paper, a cubic normal distribution defined by L-moments is suggested. This distribution is divided into six types under different combinations of third and fourth L-moment ratios. In addition, the applicable range of the proposed distribution is investigated. This distribution is then applied to structural reliability, including statistical data analysis, marginal distribution of non-Gaussian stochastic processes, and reliability index calculation. The cubic normal distribution based on L-moments has a wider application range and in the presence of extreme values, which can fit the histogram better than the one based on C-moments. Several examples are presented to demonstrate the effectiveness of the distribution in reliability engineering practices mentioned previously.