Preserving the multivariate tail measure is necessary and sufficient for a generator to recover first-order rare joint-stress probabilities and scaled conditional laws; SSGEN implements this via Pareto radial extrapolation plus a learned angular law.
It follows that In,φ≤C Z |bφn(ϕ)−φ n(ϕ)|dϕ= 2CTV bΦ(tn),Φ (tn) , We next boundI n,s
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Simulating Stress Laws under Extremal Dependence: Characterizing What Generative Models Must Preserve
Preserving the multivariate tail measure is necessary and sufficient for a generator to recover first-order rare joint-stress probabilities and scaled conditional laws; SSGEN implements this via Pareto radial extrapolation plus a learned angular law.