I fit three extreme value models to annual mamima of precipitation using the Julia library Extremes.

• Model 1: stationary
• Model 2: non-stationary with years as covariate
• Model 3: non-stationary with temperature as covariate

If you use random data, you will experience the error sometimes, but sometimes not. Below is an example, which raises the error.

What causes the error? Does the error express a failed fit? The data looks not like a GEV distribution (see images below). I appreciate any help. Thank you.

Code

using Extremes
using DataFrames


df = DataFrame(
    Year = 1950:2023,
    Precipitation = [0.495651, 0.946367, 0.546022, 0.540578, 0.534175, 0.378817, 0.757754, 0.703223, 0.476006, 0.0851862, 0.171368, 0.425137, 0.495324, 0.378817, 0.873069, 0.50048, 0.946367, 0.500415, 0.00506373, 0.341552, 0.348604, 0.546022, 0.792541, 0.341552, 0.757754, 0.419575, 0.905448, 0.00506373, 0.500415, 0.0823318, 0.143318, 0.792541, 0.104758, 0.853249, 0.789504, 0.129651, 0.50048, 0.789504, 0.946367, 0.792541, 0.546022, 0.878545, 0.792541, 0.905448, 0.513799, 0.0851862, 0.905448, 0.799792, 0.190296, 0.878545, 0.785602, 0.495324, 0.873969, 0.703223, 0.436209, 0.873069, 0.873069, 0.446525, 0.0115384, 0.341552, 0.295142, 0.617508, 0.419575, 0.905448, 0.18504, 0.842249, 0.0510619, 0.785602, 0.799792, 0.789504, 0.418074, 0.540578, 0.789504, 0.171368],
    Temperature = [0.447799, 0.613658, 0.236047, 0.518351, 0.688965, 0.0913033, 0.452838, 0.320158, 0.510309, 0.00790657, 0.00951156, 0.0939902, 0.585119, 0.0913033, 0.829481, 0.797781, 0.613658, 0.930519, 0.441482, 0.579743, 0.41028, 0.236047, 0.557033, 0.579743, 0.452838, 0.261712, 0.359162, 0.441482, 0.930519, 0.467775, 0.751947, 0.557033, 0.839668, 0.755448, 0.0485986, 0.706621, 0.797781, 0.0485986, 0.613658, 0.557033, 0.236047, 0.602792, 0.557033, 0.359162, 0.333738, 0.00790657, 0.359162, 0.870783, 0.932227, 0.602792, 0.309506, 0.585119, 0.915118, 0.320158, 0.994738, 0.829481, 0.829481, 0.301432, 0.0734843, 0.579743, 0.177626, 0.719562, 0.261712, 0.359162, 0.989634, 0.0568152, 0.599304, 0.309506, 0.870783, 0.0485986, 0.421732, 0.518351, 0.0485986, 0.00951156]
    )

fm0 = gevfit(df, :Precipitation)
fm1 = gevfit(df, :Precipitation, locationcovid = [:Year])
fm2 = gevfit(df, :Precipitation, locationcovid = [:Temperature])

Output for model 1: fm0

MaximumLikelihoodAbstractExtremeValueModel
model :
        BlockMaxima{GeneralizedExtremeValue}
        data :          Vector{Float64}[74]
        location :      μ ~ 1
        logscale :      ϕ ~ 1
        shape :         ξ ~ 1

θ̂  :    [0.515300172038444, -1.102433064656073, -0.7512065774413803]

Output for model 2: fm1

MaximumLikelihoodAbstractExtremeValueModel
model :
        BlockMaxima{GeneralizedExtremeValue}
        data :          Vector{Float64}[74]
        location :      μ ~ 1 + Year
        logscale :      ϕ ~ 1
        shape :         ξ ~ 1

θ̂  :    [1.3753214813880437, -0.00043138876235357984, -1.0913167734612388, -0.7743641862377258]

Error

ERROR: DomainError with -2.220446049250313e-16:
Exponentiation yielding a complex result requires a complex argument.
Replace x^y with (x+0im)^y, Complex(x)^y, or similar.
Stacktrace:
  [1] logpdf(d::Distributions.GeneralizedExtremeValue{Float64}, x::Float64)
    @ Distributions ~/.julia/packages/Distributions/ji8PW/src/univariate/continuous/generalizedextremevalue.jl:195
  [2] _broadcast_getindex_evalf
    @ ./broadcast.jl:709 [inlined]
  [3] _broadcast_getindex
    @ ./broadcast.jl:682 [inlined]
  [4] getindex
    @ ./broadcast.jl:636 [inlined]
  [5] macro expansion
    @ ./broadcast.jl:1004 [inlined]
  [6] macro expansion
    @ ./simdloop.jl:77 [inlined]
  [7] copyto!
    @ ./broadcast.jl:1003 [inlined]
  [8] copyto!
    @ ./broadcast.jl:956 [inlined]
  [9] copy
    @ ./broadcast.jl:928 [inlined]
 [10] materialize(bc::Base.Broadcast.Broadcasted{…})
    @ Base.Broadcast ./broadcast.jl:903
 [11] loglike(model::BlockMaxima{Distributions.GeneralizedExtremeValue}, θ::Vector{Float64})
    @ Extremes ~/.julia/packages/Extremes/4Tbee/src/structures/AbstractExtremeValueModel.jl:107
 [12] (::Extremes.var"#fobj#39"{BlockMaxima{Distributions.GeneralizedExtremeValue}})(θ::Vector{Float64})
    @ Extremes ~/.julia/packages/Extremes/4Tbee/src/parameterestimation/maximumlikelihood.jl:13
 [13] value(obj::NLSolversBase.NonDifferentiable{Float64, Vector{Float64}}, x::Vector{Float64})
    @ NLSolversBase ~/.julia/packages/NLSolversBase/kavn7/src/interface.jl:19
 [14] update_state!(f::NLSolversBase.NonDifferentiable{…}, state::Optim.NelderMeadState{…}, method::Optim.NelderMead{…})
    @ Optim ~/.julia/packages/Optim/ZhuZN/src/multivariate/solvers/zeroth_order/nelder_mead.jl:263
 [15] optimize(d::NLSolversBase.NonDifferentiable{…}, initial_x::Vector{…}, method::Optim.NelderMead{…}, options::Optim.Options{…}, state::Optim.NelderMeadState{…})
    @ Optim ~/.julia/packages/Optim/ZhuZN/src/multivariate/optimize/optimize.jl:54
 [16] optimize(d::NLSolversBase.NonDifferentiable{…}, initial_x::Vector{…}, method::Optim.NelderMead{…}, options::Optim.Options{…})
    @ Optim ~/.julia/packages/Optim/ZhuZN/src/multivariate/optimize/optimize.jl:36
 [17] optimize(f::Function, initial_x::Vector{Float64}; inplace::Bool, autodiff::Symbol, kwargs::@Kwargs{})
    @ Optim ~/.julia/packages/Optim/ZhuZN/src/multivariate/optimize/interface.jl:91
 [18] optimize
    @ ~/.julia/packages/Optim/ZhuZN/src/multivariate/optimize/interface.jl:83 [inlined]
 [19] fit(model::BlockMaxima{Distributions.GeneralizedExtremeValue}, initialvalues::Vector{Float64})
    @ Extremes ~/.julia/packages/Extremes/4Tbee/src/parameterestimation/maximumlikelihood.jl:15
 [20] fit
    @ ~/.julia/packages/Extremes/4Tbee/src/parameterestimation/maximumlikelihood.jl:40 [inlined]
 [21] gevfit(df::DataFrame, datacol::Symbol; locationcovid::Vector{…}, logscalecovid::Vector{…}, shapecovid::Vector{…})
    @ Extremes ~/.julia/packages/Extremes/4Tbee/src/parameterestimation/maximumlikelihood/maximumlikelihood_gev.jl:121
 [22] top-level scope
    @ ~/Documents/Studium/Master_Hydrologie/Masterarbeit/sub-daily-precipitation-extremes/code/ModelFitting/x.jl:13
Some type information was truncated. Use `show(err)` to see complete types.

Data distribution

Distribution of precipitation:

Distribution of temperature: