Statistical analysis and estimation of the cumulative distribution function of COVID-19 cure duration in Iraq

COVID-19 disease has aggressively affected all aspects of human life since late 2019. Hospital staff have been under unprecedented pressure from a large number of patients, and in some countries, the lack of space for patients at the height of the epidemic has reached a point where hospitals do not have the capacity to accept new patients. Therefore, studying the duration of treatment of COVID-19 patients is very important in managing the ability of treatment staff and hospital facilities. In this paper, the length of hospitalization of all COVID-19 patients in Al-Sadr General Hospital in Al-Amarah, Iraq, is statistically studied from March 2020 to April 2021. The cumulative distribution function (cdf) of the patients' treatment duration is estimated using Birnbaum-Saunders (B-S) kernel estimator. This estimate allows us to estimate the probability of a patient's stay in the hospital for a specified period of time. In this paper, we obtain an asymptotic confidence interval for the B-S kernel estimator. However, due to the dependence of the obtained confidence interval on the unknown cdf and its derivatives, we propose a bootstrap algorithm to calculate the confidence interval and use it for the length of hospital stay of COVID-19 patients.