Peaks Over Threshold (GPD) Analysis

Peaks over threshold analysis fits a generalized Pareto distribution to the amounts by which observations exceed a high threshold and uses it to estimate tail probabilities and return levels.

임계값 초과 분석은 높은 임계값을 넘은 초과량에 일반화 파레토 분포를 적합해 꼬리 확률과 재현수준을 추정하는 방법입니다.

Using all the daily data, how high will the once-in-50-years daily rainfall be?

일 강수량 전체 자료로 50년에 한 번 올 일 강수량을 추정하고 싶어요.

Peaks over threshold analysis keeps every value above a high threshold and models the excesses with a generalized Pareto distribution, which uses more extreme data than annual maxima alone. The threshold is chosen where the mean residual life plot becomes linear, and return levels combine the fitted tail with the rate of exceeding the threshold.

When to use Peaks Over Threshold (GPD) Analysis

• You have a long series of observations rather than only block maxima
• You want more precise tail estimates than annual maxima give
• You need return levels for a given number of observations per year

When to use something else

• Only one maximum per year is available; use generalized extreme value analysis
• Exceedances occur in clusters; decluster first or use a runs-based declustering method

Assumptions and requirements

• Exceedances are independent (no clustering)
• The threshold is high enough for the GPD approximation (the 95th percentile unless set); return periods are in observations unless observations per year are given
• The series is stationary

What the analysis reports

• Threshold and exceedance rate
• GPD scale and shape (ξ) with standard errors
• Return levels with delta-method confidence intervals
• Mean residual life table for threshold choice

How to report it

A generalized Pareto distribution fitted to [value] exceedances over u = [value] gave σ = [value] and ξ = [value]; the 50-year return level was [value] (95% CI [[value], [value]]).

Related methods

• Generalized Extreme Value (GEV) Analysis
• Isolation Forest Anomaly Detection

Run Peaks Over Threshold (GPD) Analysis on Quorant