Application of Smirnov Words to Waiting Time Distributions of Runs

Run and Frequency quotas for q-binary trials

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 pr…

四状态试验中连段与模式的分布研究

On distribution of runs and patterns in four state trials

该研究针对四状态独立同分布试验序列，推导了连段相关的多种分布的精确公式，可为DNA序列等四状态序列的统计分析提供理论支撑。

k阶第1、2、3、4类q负二项分布

Type $1$, $2$, $3$ and $4$ $q$-negative binomial distribution of order $k$

该研究针对概率呈几何变化的二元试验序列，利用枚举组合学推导得到k阶第1、2、3、4类q负二项分布及ℓ重叠情形下的对应分布，解决了指定长度成功游程的等待时间分布问题。