泊松分布的95%CI计算

方法1：正态近似

n=88
lambda = 47.18182
lambda+1.96*sqrt(lambda/n)

[1] 48.61699

lambda-1.96*sqrt(lambda/n)

[1] 45.74665

方法2: 精确法

X=n*lambda
c(qchisq(0.025, 2*X)/2, qchisq(0.975, 2*(X+1))/2)/n

[1] 45.75747 48.63923

示例

Say that 14 events are observed in 200 people studied for 1 year and 100 people studies for 2 years. Calculate the 95% confidence interval for Poisson mean(blogger?)

mean=14/400
mean-1.96*sqrt(mean/400)

[1] 0.01666588

mean+1.96*sqrt(mean/400)

[1] 0.05333412

c(qchisq(0.025, 2*14)/2, qchisq(0.975, 2*(14+1))/2)/400

[1] 0.01913483 0.05872405