Approximation for counts of head runs

作者：Zhang Mei^*

来源：Science China Mathematics, 2011, 54(2): 311-324.

DOI：10.1007/s11425-010-4104-6

• head run
• negative binomial distribution
• Poisson distribution
• binomial distribution
• Stein's method
• total variation distance
• coupling

In this paper, we study the count of head runs up to a fixed time in a two-state stationary Markov chain. We prove that in total variance distance, the negative binomial, Poisson and binomial distributions are appropriate approximations according to the relation of the variance and mean of the count, generalizing earlier results in previous literatures. The proof is based on Stein's method and coupling.

• 出版日期2011-2
• 单位北京师范大学