An Application of Discrete Probability Models to the Number of Outpatient Visits

ABSTRACT

It is hypothesized that the number of outpatient visits can be represented by three different probability models the truncated Poisson distribution, the Zeta distribution and the logarithmic series distribution. Maximum likelihood estimates of parameters of the above distributions were obtained by using grouped data according to the number of visits. A goodness-of-fit test was also made to compare the fit of the three distributions and the value of this statistic was classified and compared according to the types of medical care facilities. Based on the likelihood ratio statistic as a test criterion, both the truncated Poisson and Zeta distributions were not appropriate for the model of the number of outpatient visits. However, the logarithmic series distribution provides a good fit to data in the case of university hospitals, general hospitals and hospitals. When we apply this distribution in the 10 most common diseases, the estimates of the parameter vary from 0.39567 to 0.54176 for university hospitals, from 0.45329 to 0.65387 for general hospitals, and from 0.55104 to 0.77625 for hospitals. On the other hand in the case of clinics, even the logarithmic series distribution cannot be fitted to the data well. A characteristic of clinic utilization with almost homogeneous treatment patterns, in spite of the fact that there are a great many clinics, could be the reason for the above results.