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 the kernel distribution 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 results of numerical experiments and two real case studies.

翻译：本研究涉及对最大样本的概率分布估计。 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, 有限案例的模型有一定程度的错误描述。 我们建议使用内核分布估计仪的插件类型, 不需要模型性说明。 事实证明, 无症状的趋同率取决于尾数指数和第二顺序参数。 当尾巴变亮时, 参数性调整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, 只有非参数分布估计仪保持其一致性。 最后, 我们报告数字实验和两个实际案例研究的结果。