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A generalized binomial distribution determined by a two-state Markov chain and a distribution by the Bayesian approach

Research paper by M. Akahira, H. Kashima, K. Takahashi

Indexed on: 01 Mar '97Published on: 01 Mar '97Published in: Statistical Papers



Abstract

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.