CLT, MDP and LDP for Range-Renewals of I.I.D.Samplings from an Infinite Discrete Distribution

Xin-Xing Chen, Jian-Sheng Xie, Min-Zhi Zhao

Let $R_n$ be the number of distinct values of the $n$ simple samples from an infinite discrete distribution. In 1960 Bahadure proved $\displaystyle \lim_{n\to \infty} \frac{R_n}{\E…