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Add the Generalized Extreme Value (GEV) distribution, which unifies three extreme value families (Gumbel, Fréchet, Weibull) under a single shape parameter ξ.
Background
GEV(μ, σ, ξ) is the limit distribution of properly normalised maxima of i.i.d. sequences:
Summary
Add the Generalized Extreme Value (GEV) distribution, which unifies three extreme value families (Gumbel, Fréchet, Weibull) under a single shape parameter ξ.
Background
GEV(μ, σ, ξ) is the limit distribution of properly normalised maxima of i.i.d. sequences:
Scipy:
genextreme. Boost.Math does not have GEV as a named distribution.Formulas
Let z = (x - μ) / σ.
For ξ ≠ 0:
For ξ = 0 (Gumbel limit):
Delegate to
GumbelDistribution(μ, σ)from issue #54.The log-space computation
(ξ+1)·log(t)usesvector_logandvector_exp— the same SIMD primitives as Pareto and Weibull.Implementation notes
is_delegation_wrapper = false(the Fréchet and Weibull-max cases are standalone; the Gumbel case delegates).