  Percentiles and more generally, quantiles are commonly used in various
contexts to summarize data. For most distributions, there is exactly one
quantile that is unbiased. For distributions like the Gaussian that have the
same mean and median, that becomes the medians. There are different ways to
estimate quantiles from finite samples described in the literature and
implemented in statistics packages. It is possible to leverage the memory-less
property of the exponential distribution and design high quality estimators
that are unbiased and have low variance and mean squared errors. Naturally,
these estimators out-perform the ones in statistical packages when the
underlying distribution is exponential. But, they also happen to generalize
well when that assumption is violated.
