num.iterations         <- 5000
lambda.truth           <- 0.4
num.samples.per.iter   <- 1000
samples                <- numeric(num.iterations)
for(iter in seq_len(num.iterations)) {
  data            <- rpois(num.samples.per.iter, lambda.truth)
  samples[iter]   <- 2*num.samples.per.iter*(mean(data)*log(mean(data)/lambda.truth) + lambda.truth - mean(data))
}
hist(samples, freq=F, main='Histogram of LLR', xlab='sampled values of LLR values')
curve(dchisq(x, 1), 0, 20, lwd=2, xlab = "", ylab = "", add = T)