论文标题
在伯诺利的试验中，谐波成功概率不平等
On Bernoulli trials with unequal harmonic success probabilities
论文作者
论文摘要
研究了具有不平等谐波成功概率的Bernoulli方案，以及其一些自然扩展。该研究包括在某个时间窗口中的成功数量，连续成功之间的时代以及第一个成功的时间。讨论了大型样本渐近学，统计参数估计以及与Sibuya分布和Yule-Simon分布的关系。该玩具模型在几种应用中相关，包括可靠性，物种抽样问题，创纪录的值打破和随机步行而与灾难进行随机步行。
A Bernoulli scheme with unequal harmonic success probabilities is investigated, together with some of its natural extensions. The study includes the number of successes over some time window, the times to (between) successive successes and the time to the first success. Large sample asymptotics, statistical parameter estimation, and relations to Sibuya distributions and Yule-Simon distributions are discussed. This toy model is relevant in several applications including reliability, species sampling problems, record values breaking and random walks with disasters.
