二项分布两种近似计算的讨论

Discussion about Two Approximate Calculations of Binomial Distribution

泊松定理、隶莫佛-拉普拉斯定理给出了二项分布的近似计算公式.如何把握近似条件使近似更为准确?通过二项分布、泊松分布、正态分布的概率值的对比,得出泊松分布在p较小时、n不用太大即可近似较好;正态分布在p较小、n较大等三种条件下都能较好近似二项分布;在p较小、n足够大时两种近似均可的结论.

Poisson theorem and De Moivre - Laplace theorem present the approximate calculation formula of binomial distribution. How can we master the approximate conditions in order to make the approximate more accurate？ According to the comparison of the probability of binomial distribution, normal distribution and Poisson distribution, an inclusion is drawn, which goes like this：Poisson distribution approximates binomial distribution better with smaller p and not very big n;normal distribution does with three conditions including smaller p and bigger n; both do with smaller p and big enough n.