Generalized Extreme Value (GEV) Analysis

Generalized extreme value analysis fits the GEV distribution to block maxima, such as annual maximum rainfall, by maximum likelihood and estimates return levels for long return periods.

일반화 극값 분석은 연 최댓값 같은 블록 최댓값에 GEV 분포를 최대우도로 적합해 긴 재현기간의 재현수준을 추정하는 방법입니다.

What is the 100-year flood level estimated from these annual maximum river levels?

연 최고 수위 자료로 100년 빈도 홍수위를 추정하고 싶어요.

The GEV distribution unifies the Gumbel, Fréchet and Weibull limits for block maxima through a location, a scale and a shape parameter ξ. Fitting it to annual or other block maxima gives return levels, the value exceeded on average once every T blocks, with confidence intervals that widen quickly for long return periods.

When to use Generalized Extreme Value (GEV) Analysis

• You have one maximum per block such as per year
• You need return levels for design or risk assessment
• At least about 20–30 blocks of data are available

When to use something else

• You have the full daily series and want to use more extremes; use peaks over threshold (GPD) analysis
• The extremes have a clear trend; use a non-stationary GEV model with covariates

Assumptions and requirements

• Block maxima are independent and identically distributed
• Blocks are long enough for the extreme value limit to apply
• No trend over time (stationarity)

What the analysis reports

• Location, scale and shape (ξ) estimates with standard errors
• Return levels for chosen return periods with delta-method confidence intervals
• Likelihood-ratio test of the Gumbel case ξ = 0
• Goodness-of-fit check

How to report it

A GEV distribution fitted to [value] annual maxima gave μ = [value], σ = [value] and ξ = [value]; the 100-year return level was [value] (95% CI [[value], [value]]).

Related methods

• Peaks Over Threshold (GPD) Analysis
• Weibull Parametric Survival Model

Run Generalized Extreme Value (GEV) Analysis on Quorant