一阶移动平均线最大值的分布：离散情形
The distribution of the maximum of a first order moving average: the discrete case
摘要：
我们给分布的$M_n$，最大的序列的$n$观察从一个移动平均的顺序1。首先给出的解决方案中的重复积分，然后为潜在的独立随机变量是离散的情况下。当相关性为正时，$$ P(M_n \max^n_{i=1} X_i \leq x) = \sum_{j=1}^\infty β_{jx} ν_{jx}^{n} \approx B_{x} r{1x}^{n} $$其中$\{ν_{jx}\}$是某个矩阵的特征值，$r_{1x}$是特征值的最大幅度，而$I$取决于基础随机变量的可能值的数量。本征值不依赖于$x$，仅依赖于它的范围。
英文摘要：
We give the distribution of $M_n$, the maximum of a sequence of $n$ observations from a moving average of order 1. Solutions are first given in terms of repeated integrals and then for the case where the underlying independent random variables are discrete. When the correlation is positive, $$ P(M_n \max^n_{i=1} X_i \leq x) = \sum_{j=1}^\infty β_{jx} ν_{jx}^{n} \approx B_{x} r{1x}^{n} $$ where $\{ν_{jx}\}$ are the eigenvalues of a certain matrix, $r_{1x}$ is the maximum magnitude of the eigenvalues, and $I$ depends on the number of possible values of the underlying random variables. The eigenvalues do not depend on $x$ only on its range.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
