Parametric Estimation And Hypothesis Test About Sampling Model Without Replacement In Finite Population With Bernoulli Distribution

This paper focuses on parameter estimation and hypothesis test about the sampling model without replacement in finite population with Bernoulli distribution. The study includes two parameters of population:number of population N, number of individuals with some properties in popuation M. The expressions of sample joint probability mass function is introduced, and the maximum likelihood estimates of the parameter N and M are deduced and compared with other point estimation methods. Based on the hypergeometric distribution, the exact confidence interval of parameter M is proved anew and the exact confidence intervals of parameter N is proposed, whose efficiency is proved on confidence level and superiority and compared with other confidence intervals. The uniformly most powerful (UMP) tests for parameters N and M are proved based on Neyman-Pearson lemma with the sample joint probability mass function. Finally, application of the above conclusions is illustrated through some examples.