Joint distributions of numbers of success-runs and failures until the first consecutivek successes
Joint distributions of numbers of success-runs and failures until the first consecutivek successes
复制标题
成功运行和失败次数的联合分布，直到第一个连续 k 次成功
DOI：
10.1007/bf00773459
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发表时间：
1995
影响因子：
1
通讯作者：
K. Hirano
中科院分区：
文献类型：
--
作者：
S. Aki;K. Hirano
对于独立同分布的整数值随机变量序列、{0,1}值马尔可夫链和有序二进制序列，得到了失败次数、成功次数和连续成功次数小于等于连续成功次数的联合分布。有几种方法可以计算指定长度的运行次数。本文研究了基于三种计算运行次数的联合分布，即指定长度的重叠运行次数、指定长度的非重叠运行次数和指定长度及以上的运行次数。它们的边际分布可以立即得到，而且大多数都非常简单。
Joint distributions of the numbers of failures, successes and success-runs of length less thankuntil the first consecutiveksuccesses are obtained for some random sequences such as a sequence of independent and identically distributed integer valued random variables, a {0, 1}-valued Markov chain and a binary sequence of orderk. There are some ways of counting numbers of runs with a specified length. This paper studies the joint distributions based on three ways of counting numbers of runs, i.e., the number of overlapping runs with a specified length, the number of non-overlapping runs with a specified length and the number of runs with a specified length or more. Marginal distributions of them can be derived immediately, and most of them are surprisingly simple.