论文标题
关于四个州试验中的跑步和模式的分布
On distribution of runs and patterns in four state trials
论文作者
论文摘要
从数学和统计的角度来看，DNA链的一段可以看作是四态（A，C，G，T）试验的序列。我们考虑与多状态序列的运行长度相关的运行和模式的分布，尤其是对于四个状态（a，b，c，d）。令$ x_ {1}，x_ {2}，\ ldots $为四个状态i.i.d. \ \试验的序列，以$ \ mathscr {s} = \ {a，\ b，\ b，\ c，\ c，\ c，\ c，\ c，\ d \} $的四个符号的四个符号，带有可能性$ p（a） $ p（c）= p_ {c} $和$ p（d）= p_ {d}，$。在本文中，我们获得了B的运行概率分布功能的确切公式，即“订单$ k $的离散分布，最长的运行统计信息，最短的运行统计信息，等待时间分布，等待时间分布和运行长度的分布”。
From a mathematical and statistical point of view, a segment of a DNA strand can be viewed as a sequence of four-state (A, C, G, T) trials. We consider distributions of runs and patterns related to run lengths of multi-state sequences, especially for four states (A, B, C, D). Let $X_{1}, X_{2}, \ldots$ be a sequence of four state i.i.d.\ trials taking values in the set $\mathscr{S}=\{A,\ B,\ C,\ D\}$ of four symbols with probability $P(A)=P_{a}$, $P(B)=P_{b}$, $P(C)=P_{c}$ and $P(D)=P_{d},$ respectively. In this paper, we obtain exact formulae for the probability distribution function for runs of B's the discrete distribution of order $k$, longest run statistics, shortest run statistics, waiting time distribution and the distribution of run lengths.
