A generalized binomial distribution determined by a two-state Markov chain and a distribution by the Bayesian approach
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- 作者：M. Akahira (1)
H. Kashima (2)
K. Takahashi (3) - 关键词：Key Words Bernoulli random variables ; Markov chain ; asymptotic distribution ; negative hypergeometric distribution
- 刊名：Statistical Papers
- 出版时间：March 1997
- 出版年：1997
- 期刊代码：pc624_0932-5026
- 类别：mat
- 卷：38
- 期：1
- 页码：27-42
- 数据来源：sp
摘要
For dependent Bernoulli random variables, the distribution of a sum of the random variables is obtained as a generalized binomial distribution determined by a two-state Markov chain. Asymptotic distributions of the sum are derived from the central limit theorem and the Edgeworth expansion. A numerical comparison of the exact and asymptotic distributions of the sum is also given. Further a distribution of the sum by the Bayesian approach is derived and its asymptotic distributions are provided. Numerical results are given.