Sooner and later waiting time problems for success and failure runs in higher order Markov dependent trials
Sooner and later waiting time problems for success and failure runs in higher order Markov dependent trials
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成功和失败的迟早等待时间问题在高阶马尔可夫相关试验中运行
DOI：
10.1007/bf00052332
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发表时间：
1996
影响因子：
1
通讯作者：
S. G. Mohanty
中科院分区：
文献类型：
--
作者：
S. Aki;Narayanaswamy Balakrishnan;S. G. Mohanty
利用概率母函数法和组合方法，导出了二阶马氏相依试验中第一次成功运行时间的概率母函数，以及成功运行时间与失败运行时间之间的前一次运行时间和后一次运行时间的概率母函数.进一步给出了m阶马氏相依试验中等待时间的2.m条件概率母函数方程组。由于方程组关于条件概率母函数是线性的，因此可以精确求解，从而得到等待时间分布的概率母函数。如果m很大，一些计算机代数系统可用于求解线性方程组。
The probability generating functions of the waiting times for the first success run of length k and for the sooner run and the later run between a success run of length k and a failure run of length r in the second order Markov dependent trials are derived using the probability generating function method and the combinatorial method. Further, the systems of equations of 2.mconditional probability generating functions of the waiting times in the m-th order Markov dependent trials are given. Since the systems of equations are linear with respect to the conditional probability generating functions, they can be solved exactly, and hence the probability generating functions of the waiting time distributions are obtained. If m is large, some computer algebra systems are available to solve the linear systems of equations.