Application of generalized Pareto distribution for modeling aleatory variability of ground motion

Abstract

The lognormal distribution is commonly used to characterize the aleatory variability of ground-motion prediction equations (GMPEs) in probabilistic seismic hazard analysis (PSHA). However, this approach often leads to results without actual physical meaning at low exceedance probabilities. In this paper, we discuss how to calculate PSHA with a low exceedance probability. Peak ground acceleration records from the NGA-West2 database and 15,493 residuals calculated by Campbell-Bozorgnia using the NGA-West2 GMPE were applied to analyze the tail shape of the residuals. The results showed that the generalized Pareto distribution (GPD) captured the characteristics of residuals in the tail better than the lognormal distribution. Further study showed that the shapes of the tails of the distributions of residuals with different magnitudes varied significantly due to the heteroscedasticity of the magnitude; the distribution of residuals with larger magnitudes had a smaller upper limit on the right side. Moreover, the residuals of the three magnitude ranges given in this study were more consistent with the GPD of different parameters at the tail than the lognormal distribution and the GPD fitted by all the residuals, leading to a bounded PSHA hazard curve. Therefore, the lognormal distribution is more representative up to a determined threshold, and the GPD fitted to the residuals of three ranges of magnitude better characterizes the tail for PSHA calculation.

GNSS integrity risk evaluation in the position domain based on the generalized Pareto distribution

“…The issue with efficiently characterizing the tail stems from the fact that more samples are required to make useful and confident statements on the error distribution. Many researchers have noted that a Gaussian distribution fails to efficiently characterize large errors that occur more frequently than predicted by model [16]. In contrast, a GPD can relieve the need for a strong a priori Gaussian distribution.…”

Derivation of a Formula for Mountain Height as a Function of Rank in Height

“…If the true distribution is unknown but belongs to a large class of distributions, the Pickands-Balkema-De Haan theorem [42] [43] [44] implies that the tail of the distribution above a large threshold value is well-approximated by a generalized Pareto distribution. For the present problem, as h min is the threshold value and mountain heights are restricted to the interval [ ] min max , h h , the generalized Pareto distribution P GP has a finite right endpoint and has the form [42] [44]:…”