论文标题
某些离散流程的订单统计数据的振荡
Oscillations for order statistics of some discrete processes
论文作者
论文摘要
假设$ k $ balls以均匀的概率独立地将$ n $ box放到$ n $盒中，其中$ n，k $较大，比率大约等于某些正面$λ$。最大盒子计数具有违反直觉的行为：首先，具有高概率，最多需要两个值$ m_n $或$ m_n+1 $，其中$ m_n $大约是$ \ frac {\ ln n} {\ ln \ ln \ ln n n} $。此外，它以异常周期性在这两个值之间振荡。为了证明此语句和各种概括，首先表明，对于$ x_1，...，x_n $独立且分布式分布式分布式离散随机变量，带有共同分布$ f $，在轻度条件下，根据分布的尾巴，在三个可能的家族中的最大振荡限制了其最大振荡。结果是在各种分配问题中的合奏对秩序统计的等效性，这是通过调节极限理论获得的。还提供了有关最大关系以及应用程序的关系数量的结果。
Suppose $k$ balls are dropped into $n$ boxes independently with uniform probability, where $n, k$ are large with ratio approximately equal to some positive real $λ$. The maximum box count has a counterintuitive behavior: first of all, with high probability it takes at most two values $m_n$ or $m_n+1$, where $m_n$ is roughly $\frac{\ln n}{\ln \ln n}$. Moreover, it oscillates between these two values with an unusual periodicity. In order to prove this statement and various generalizations, it is first shown that for $X_1,...,X_n$ independent and identically distributed discrete random variables with common distribution $F$, under mild conditions, the limiting distribution of their maximum oscillates in three possible families, depending on the tail of the distribution. The result stated at the beginning follows from the equivalence of ensemble for the order statistics in various allocations problems, obtained via conditioning limit theory. Results about the number of ties for the maximum, as well as applications, are also provided.
