Statistical inference for discrete distributions on random sequences

研究了随机序列上某些模式和扫描的出现次数和等待时间的精确离散分布。根据我们的理论新结果，我们可以对成功概率等参数进行统计推断。通过对条件概率生成函数方法的扩展，得到了新的解析结果，其中一些结果也适用于数值计算。

Exact discrete distributions of numbers of occurrences and waiting times of some patterns and scans on random sequences are investigated. Based on our theoretical new results we can make statistical inference of some parameters such as success probability. By extending the method of conditional probability generating functions we have derived new results analytically, some of which are also suitable for numerical calculations.