On the statistical estimation of the lifetimes of charmed particles

Various statistical methods for the estimation of the mean lifetimes of charmed particles have been considered. It is shown that the usual estimates of the maximum likelihood in some cases do not exist or may have rather great positive bias, if the statistics are low. Alternative estimates of the mean lifetime τ are discussed. Among them the “jackknife” estimate of τ is considered. The minimum variance unbiased estimates of the average rate of decay have been derived for some particular cases. It is also shown that the usual estimate of the ratio of the mean lifetimes of different kinds of particles may also have a bias when the statistics are poor. Two methods of reducing this bias have been proposed.