二项分布近似计算的误差量化分析

Quantitative Analysis of Approximate Calculation Errors of Binomial Distribution

试验次数较大时,二项分布可用正态分布或泊松分布作近似计算.对于系统可靠度问题,量化分析了随机变量上下限、整数端点对近似计算的累计误差影响,发现用正态分布作近似时累计误差总为负数且在期望附近达到最大,对整数边界点进行扩张修正可提高估算精度;对不同参数组合的误差量化分析表明,当期望小于10时用泊松分布近似计算效果较好,当期望超过10后用正态分布作近似效果较好.

When the number of tests is large,the binomial distribution can be approximated by normal distribution or Poisson distribution.For the system reliability problem,this paper quantifies the cumulative error of the approximation that is influenced by the upper and lower bounds of the random variable and the endpoint.It is found that the cumulative error is always negative when approximated by normal distribution and reaches the maximum near expectation.Expansion correction of integer boundary points can improve estimation accuracy.Quantitative analysis of errors for different parameter combinations shows that Poisson distribution is suitable for the case that the expectation is less than 10,and the approximation effect of normal distribution is better when the expectation exceeds 10.