Dissertation (Msc. Statistics)Health care is essential to the general welfare of society. Studying the hospital patients' data distribution through the probability distribution analysis and forecasting time series model is very important in the health care system. This study has examined the hospital inpatients and outpatients' daily data for two years taken from DRRH through the hospital electronic health management information system. This study seeks to identify comprehensively the appropriate statistical distributions on inpatient and outpatient data of the DRR hospital. Primary fitting of the distributions to inpatient and outpatient data was performed by the Easyfit 5.5 Profession statistical software. The software deals with 61 continuous distributions, including three goodness of fit test for raw data and two for frequency data. Kolmogorov- Smirnov test, Anderson- Darling test and Chi-Square test only for raw data. The parameters of the selected distributions were estimated by the maximum likelihood method. The final selection of fittest distribution was done with respect to the minimum calculated value of log-likelihood and hence AIC and BIC values. The research work revealed that Generalized Extreme Value distribution is the best-fit distribution model for the hospital inpatient daily data. Also, the Dagum distribution followed by Log logistic (3P) distribution was selected to be the best-fit distribution model representing the hospital outpatients' daily data. The study identified ARIMA (1, 1, 0) model as the best predictive model for the daily average number of outpatients visiting the hospital outpatient department for two years. In order to prepare adequate facilities for the overwhelming outpatients in the outpatient department at the hospital, the DRRH administration should make use of the probability distributions and forecasted figures to plan further development activities for the hospital.