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Explanation:
Option A is correct. Under Extreme Value Theory (EVT), the Pickands-Balkema-de Haan theorem states that for a broad class of underlying distributions, as the threshold is raised, the distribution of exceedances over that high threshold asymptotically converges to a Generalized Pareto Distribution (GPD).
Option B is incorrect because if the tail parameter approaches zero (not infinity), the GEV converges to the Gumbel distribution (light-tailed).
Option C is incorrect because EVT is generally non-parametric with respect to the underlying distribution's body and does not require the loss distribution to be specifically normal or lognormal.
Option D is incorrect because as the threshold decreases, the number of exceedances increases, but setting the threshold too low introduces bias because the asymptotic approximation (GPD) may not accurately fit the data in the center of the distribution.
A
As the threshold value is increased, the distribution of losses over a fixed threshold value converges to a generalized Pareto distribution.
B
If the tail parameter value of the generalized extreme-value (GEV) distribution goes to infinity, then the GEV essentially becomes a normal distribution.
C
To apply EVT, the underlying loss distribution must be either normal or lognormal.
D
The number of exceedances decreases as the threshold value decreases, which causes the reliability of the parameter estimates to increase.
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