Statistical Inference in Bernoulli Trials with Dependence
具有依赖性的伯努利试验中的统计推断
A model for Bernoulli trials with Markov dependence is developed which possesses the usual frequency parameter $p = P\lbrack X_i = 1\rbrack$ and an additional dependence parameter $\lambda = P\lbrack X_i = 1 \mid X_{i-1} = 1\rbrack$. Sufficient statistics for the model with $p$ and $\lambda$ unknown are found and an exact closed form expression for their small sample joint distribution is given. Large sample distribution theory is also given and small sample variances…