This study concerns probability distribution estimation of sample maximum. The traditional approach is the parametric fitting to the limiting distribution - the generalized extreme value distribution; however, the model in finite cases is misspecified to a certain extent. We propose a plug-in type of nonparametric estimator which does not need model specification. It is proved that both asymptotic convergence rates depend on the tail index and the second order parameter. As the tail gets light, the degree of misspecification of the parametric fitting becomes large, that means the convergence rate becomes slow. In the Weibull cases, which can be seen as the limit of tail-lightness, only the nonparametric distribution estimator keeps its consistency. Finally, we report the results of numerical experiments.

翻译：本研究涉及对样本最大值的概率分布估计。 传统方法是与限制分布相匹配的参数性参数性( 普遍极端值分布); 但是, 有限情况下的模型有一定程度的错误描述。 我们提出一个不需模型规格的非参数性估计值的插件型, 不需要模型规格。 事实证明, 无参数性趋同率取决于尾数指数和第二顺序参数。 当尾数变亮时, 参数性装配的偏差程度变得很大, 这意味着趋同率变得缓慢。 在可被视为尾光极限的Weibull案例中, 只有非参数性分布估计值保持其一致性。 最后, 我们报告数字实验的结果。