In radiation therapy with hadron beams, it is important to evaluate the range of incident ions and the deposited dose distribution in a patient body for the effective utilization of such properties as the dose concentration and the biological effect around the Bragg peak. However, there is some ambiguity in determining this range because of a conversion error from the x-ray CT number to the charged particle range. This is because the CT number is related to x-ray absorption coefficients, while the ion range is determined by the electron density of the substance. Using positron emitters produced in the patient body through fragmentation reactions during the irradiation has been proposed to overcome this problem. The activity distribution in the patient body can be deduced by detecting pairs of annihilation gamma rays emitted from the positron emitters, and information about the range of incident ions can be obtained. In this paper, we propose a quantitative comparison method to evaluate the mean range of incident ions and monitor the activity distribution related to the deposited dose distribution. The effectiveness of the method was demonstrated by evaluating the range of incident ions using the maximum likelihood estimation (MLE) method and Fisher's information was calculated under realistic conditions for irradiations with several kinds of ions. From the calculated Fisher's information, we compared the relative advantages of initial beams to determine the range of incident ions. The (16)O irradiation gave the most information among the stable heavy ions when we measured the induced activity for 500 s and 60 s just after the irradiation. Therefore, under these conditions, we concluded that the (16)O beam was the optimum beam to monitor the activity distribution and to evaluate the range. On the other hand, if the positron emitters were injected directly as a therapeutic beam, the (15)O irradiation gave the most information. Although the relative advantages of initial beams as well as the measured activity distributions slightly varied according to the measurement conditions, comparisons could be made for different conditions by using Fisher's information.