I am currently studying statistical hypothesis testing, specifically the Likelihood Ratio Test (LRT), and I've come across a problem that I'm struggling to solve. I would greatly appreciate any guidance or help.
The problem involves two independent random variables, $Y_1$ and $Y_2$, each following a Poisson distribution with parameters $\lambda_1$ and $\lambda_2$ respectively, where $\lambda_1, \lambda_2 > 0$.
The null hypothesis ($H_0$) is that $\lambda_1 > \lambda_2$. I need to formulate a likelihood ratio test for this hypothesis.
I understand the basic concept of the LRT, which involves comparing the likelihood of the observed data under the null hypothesis to the likelihood of the observed data under the alternative hypothesis. However, I'm having trouble applying this concept to the specific case of Poisson distributions.
Any help in understanding how to formulate this test would be greatly appreciated. Thank you in advance!