Hi,
After some thought, I found the treatment of sample mean equal 0 was not
appropriate. I modified the function likelihood.ratio.test.Poisson.
resulting.matrix now has 0.0512 as the average of type I error.
function(lambda, sample.size, significance.level)
{
reject <- 0
sample.mean <- mean(rpois(sample.size, lambda))
if (sample.mean == 0)
{
test.statistics <- 2 * sample.size * lambda
}
else
{
test.statistics <- 2 * sample.size * (lambda - sample.mean + sample.mean
* log(sample.mean / lambda))
}
if (test.statistics >= qchisq(1 - significance.level, 1)) {reject <- 1}
else {reject <- 0}
return(reject)
}
> for (i in 1:500){
+ resulting.matrix[i,1] <- 0.01 * i
+ resulting.matrix[i,2] <- mean(sapply(1:100,function(x)
likelihood.ratio.test.Poisson(0.01*i,10,0.05)))
+ }
> mean(resulting.matrix[,2])
[1] 0.05102
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