I'm doing an experiment where I'm measuring the mean-lifetime of muons. I have a set of data points for the number of decays against time, resembling an exponential distribution (of course). But in the experiment, there weren't a lot of counts measured (approximately 500) so for some time-values I got zero counts where it doesn't really fit to the exponential distribution.
I was wondering if it is justifiable to remove these points and what the reasoning behind that is. It's a much better fit if I do remove them compared to the experimental value of the muon lifetime given by e.g. Source- M. Tanabashi et al. (Particle Data Group), Review of Particle Physics, Phys. Rev. D 98, 030001 (2018)