# Likelihood ratio test in Poisson distribution

I have a dataset that describe the number of passengers that fly with an airline per day. The airline guesses that on average 1300 passengers fly per day and I want to test this hypothesis using a likelihood ratio test.

My first thought was to set the hypotheses: H0: λ = 1300 and H1: λ <>1300. According to wikipedia the likelihood ratio test is: -2ln(likelihood for null model) + 2ln(likelihood for alternative model).

Using R I can find the likelihood of the null hypothesis but how can I calculate the likelihood for the alternative hypothesis in a Poisson distribution?

Thanks

• Poisson assumes the number of passengers is the aggregation of 1300 independent but identical events. Do you think it's possible that trips are not iid... such as the first day of spring break? – RegressForward Jun 10 '15 at 16:37
• Is this for a class? – Glen_b Jun 11 '15 at 11:27

You find the MLE of $\lambda$ and then compute the log-likelihood at that value of $\lambda$ (and multiply by -2)