Fitting generalized Pareto distribution based on the expected order statistics and its application for ice accretion hazard mapping. (March 2023)

• Record Type: Journal Article
• Authors: Liu, Y.X.; Sheng, C.; Hong, H.P.
• Is Part Of: Structural safety. Volume 101(2023)
• Publication Date: 2023-03
• Subjects: Distribution fitting method -- Nonlinear least-squares method -- Generalized Pareto distribution -- Ice accretion thickness -- Hazard -- Wind-on-ice load; Structural stability -- Periodicals; Safety factor in engineering -- Periodicals; Reliability (Engineering) -- Periodicals; Constructions -- Stabilité -- Périodiques; Coefficient de sécurité en ingénierie -- Périodiques; Fiabilité -- Périodiques; 620.86
• DOI: 10.1016/j.strusafe.2022.102297
• Languages: English
• ISSNs: 0167-4730

Abstract

Highlights: Proposed a nonlinear least-squares fitting method for generalized Pareto distribution (GPD). Proposed method considers expected order statistics to estimate location, scale, and shape parameters. Compared the performance of the proposed method and some well-known existing methods. Using the peak-over-threshold (POD) approach with GPD assessed the Canadian ice accretion hazard. Developed ice accretion hazard maps and the companion load factor for wind-on-ice load. Abstract: The extreme value analysis of the ice accretion thickness can be carried out based on the peaks-over-threshold (POT) approach to take advantage of the available rare samples in assessing the ice accretion thickness hazard. For the POT approach, the generalized Pareto distribution (GPD) with location, scale, and shape parameters has been frequently employed, although the estimators of parameters of GPD by using existing fitting methods could be associated with significant bias or variability. In the present study, we propose a new nonlinear least-squares fitting method by considering the expected order statistics. We compare its performance with some existing methods through simulation analysis, showing that the proposed method outperforms some well-known existing methods for a range of values of the shape parameter. We then apply the POT approach with GPD as well as the block maximum approach with Gumbel distribution to estimate T -year return period value of the annual maximum ice accretion thickness, xT, for Canadian sites. The analysis results indicate that xT is sensitive to whether the POT or the annual maximum approach with Gumbel distribution is employed. For the considered cases, the use of GPD fitted to POT values is preferred. Also, based on the wind-on-ice analysis results, it is suggested a companion wind load factor of about 0.5 to 0.55 could be adopted.