  During an epidemic outbreak of a new disease, the probability of dying once
infected is considered an important though difficult task to be computed. Since
it is very hard to know the true number of infected people, the focus is placed
on estimating the case fatality rate, which is defined as the probability of
dying once tested and confirmed as infected. The estimation of this rate at the
beginning of an epidemic remains challenging for several reasons, including the
time gap between diagnosis and death, and the rapid growth in the number of
confirmed cases. In this work, an unbiased estimator of the case fatality rate
of a virus is presented. The consistency of the estimator is demonstrated, and
its asymptotic distribution is derived, enabling the corresponding confidence
intervals (C.I.) to be established. The proposed method is based on the
distribution F of the time between confirmation and death of individuals who
die because of the virus. The estimator's performance is analyzed in both
simulation scenarios and the real-world context of Argentina in 2020 for the
COVID-19 pandemic, consistently achieving excellent results when compared to an
existing proposal as well as to the conventional \naive" estimator that was
employed to report the case fatality rates during the last COVID-19 pandemic.
In the simulated scenarios, the empirical coverage of our C.I. is studied, both
using the F employed to generate the data and an estimated F, and it is
observed that the desired level of confidence is reached quickly when using
real F and in a reasonable period of time when estimating F.
