论文标题
Q-二进制试验的运行和频率配额
Run and Frequency quotas for q-binary trials
论文作者
论文摘要
我们研究了等待时间的分布，以$ q $ - 索恩的变化以及后来等待时间问题。一种变化在成功和失败的运行中施加了长度和频率配额。另一个案例考虑了二进制试验，其概率在几何上有所不同。我们还研究了在相同变化下最长运行的分布。主要定理是较早的等待时间问题，以及最长成功的长度的联合分布，而最长的失败会在成功和失败的运行中施加的运行和频率配额时。在目前的工作中，我们考虑了一系列独立的二进制$（0-1）$试验的序列，这些序列不一定与几何规则变化的概率相同。通过枚举组合制剂获得的分布的确切公式。
We study the distributions of waiting times in variations of the $q$-sooner and later waiting time problem. One variation imposes length and frequency quotas on the runs of successes and failures. Another case considers binary trials for which the probability of ones is geometrically varying. We also study the distributions of Longest run under the same variations. The main theorems are sooner and later waiting time problem and the joint distribution of the length of the longest success and longest failure runs when a run and frequency quotas imposed on runs of successes and failure. In the present work, we consider a sequence of independent binary $(0-1)$ trials with not necessarily identical distributed with probability of ones varying according to a geometric rule. Exact formulae for the distributions obtained by means of enumerative combinatorics.
