问题如下：
Let X be a random variable representing the daily loss of your portfolio. The "peaks over threshold" (POT) approach considers a threshold value, u, of X and the distribution of excess losses over this threshold. Which of the following statements about this application of extreme value theory is correct?
选项：
A. To apply the POT approach, the distribution
of X must be elliptical and known.
B. If X is normally distributed, the
distribution of excess losses requires the estimation of only one parameter, β,
which is a positive scale parameter.
C. To apply the POT approach, one must choose a
threshold, u, which is high enough that the number of observations in excess of
u is zero.
D. As the threshold, u, increases, the
distribution of excess losses over u converges to a generalized Pareto
distribution.
解释：
D is correct.
考点: Extreme Value
解析: The distribution of excess losses over u converges to a generalized Pareto distribution as the threshold value u increases.
The distribution of X itself can be any of the commonly used distribution: normal, lognormal, t, etc., and will usually be known. The distribution of excess losses requires the estimation of two parameters, a positive scale parameter β and a shape or tail index parameter ξ. One must choose a threshold u that is high enough so that the theory applies but also low enough so that there are observations in excess of u.
n增大，POT不是更趋近于广义极值理论吗？POT本身就是广义帕累托，怎么能说趋近呢？
