关于二项分布的泊松近似计算问题

On Poisson Approximation of Binomial Distribution

当n充分大,nP很小时,二项分布近似于参数为λ=nP的泊松分布,计算结果表明,在X区间[0,nP+2σ]内,泊松拟合值才能近似代替二项分布数据。本文利用最小二乘多项式拟合方法求得在不同参数n和P下的泊松近似修正系数,修正后的泊松拟合值与二项分布数据有很好的近似。

When the parameter n of binomial distribution is enough large and the product of parameters nP is very small, binomial distribution approaches Poisson distribution (λ=nP). The calculation shows that only in the range of [0, nP=2σ] can Poisson fitting value replace binomial distribution value. This paper makes use of least square polynomial fitting method to obtain the approximate modified coefficients of Poisson in the distinct system of parameters. There is a very close approximation between the modified Poisson fitting value and the binomial distribution value.