摘要
目的建立含区间数据Gamma分布的参数估计方法,并用于SARS潜伏期的推算.方法采用EM算法构造出求解含区间数据Gamma分布参数极大似然估计的迭代公式,并应用于SARS潜伏期分布的拟合.结果基于EM算法的极大似然估计方法可以计算出含区间数据Gamma分布的两个参数,从而得到均值估计.同时,还可以根据极大似然估计的渐近性质,计算出估计量的标准误及各参数的置信区间.用于中国内地SARS爆发资料分析,发现SARS潜伏期服从Gamma(2.1,2.33)分布;潜伏期均值和方差的极大似然估计值分别为4.89天(95%CI 4.43～5.35)和11.40天2;95%的病人感染SARS-CoV后将在11.42天内发病.结论基于EM算法的极大似然估计方法对于含区间数据Gamma分布参数的估计是强健的,可以用于含区间数据SARS潜伏期的精确估计.
Objective To develop a method to estimate the two parameters of Gamma distribution with interval data and conduct that to estimate the length of incubation period of severe acute respiratory syndrome (SARS).Methods EM algorithm was employed to construct an iterative formula for solving the maximum likelihood estimation (MLE) of parameters of Gamma distribution with interval data,whereby we can estimate the distribution parameters of SARS incubation period with interval data.Results The two parameters of Gamma distribution with interval data can be estimated by MLE based on EM algorithm,whereby the estimation of the mean can be obtained.Meanwhile,the standard error and the confidence interval for each parameter also can be calculated by using the asymptotic property of MLE.The data of SARS outbreak from mainland of China in 2003 analyzed by above method found that SARS incubation period had a Gamma (2.10,2.33) distribution; MLE of the mean and variance of SARS incubation period was 4.89 days (95% confidence interval 4.43-5.35) and 11.40 days 2,respectively; therefore 95% of SARS patients would experience the onset of symptoms within 11.42 days.Conclusion MLE based on EM algorithm is robust for parameter estimation of Gamma distribution with interval data and can be employed to estimate the distribution parameters of SARS incubation period with interval data.
出处
《中国卫生统计》
CSCD
北大核心
2005年第2期71-73,79,共4页
Chinese Journal of Health Statistics
基金
上海市科委非典防治专项科研基金(NK2003-002)
教育部防治非典科技攻关项目(No.10)资助
关键词
GAMMA分布
参数估计
EM算法
传染性非典型肺炎
潜伏期
Parameter estimation of Gamma distribution,EM algorithm,Severe acute respiratory syndrome,Incubation period
