Normal approximation to the hypergeometric distribution in nonstandard cases and a sub-Gaussian Berry–Esseen theorem

摘要: Abstract In this paper, we consider simple random sampling without replacement from a dichotomous finite population. We investigate accuracy of the Normal approximation to Hypergeometric probabilities for wide range parameter values, including nonstandard cases where fraction tends one and proportion objects interest in population boundary zero one. establish non-uniform Berry–Esseen theorem distribution which shows that cases, rate can be considerably slower than Binomial distribution. also report results moderately large numerical study provide some guidelines using samples.