Abstract: Aiming at two groups of samples from different populations in the pharmacokinetics, we developed a comparative test of two groups. Firstly, we provided the likelihood function when the null hypothesis and the alternative hypothesis are given. Then the likelihood ratio statistic is constructed, and we proved that the limit distribution of the statistic is $\chi^{2}(3)$ when null hypothesis is true. Lastly the numerical simulation is conducted to confirm the truth of the theory through data verification. The results show that for the two groups with the same parameters, the empirical distribution and the limit distribution fitting well when the sample size is large.  On the contrary, the more differences  parameters with the smaller values of the $p$-value, and the evidence to refuse the null hypothesis will be more sufficient.

Key words: concentration-time curves, change point, comparative test of two groups