Using analytical and numerical methods, estimates are given of future predictions in astrophysics that can be gathered from a sequence of observed events, for example for γ -ray bursts. Some general probability considerations are provided and then a maximum likelihood estimation, together with an approximation for the large number limit of possible events. Illustrations are given of the numerical maximum likelihood estimation programs in the situations of both a large number and a finite number of events. The effects of data uncertainty are also considered. Numerical calculations and comparisons with theoretical expectations are presented too.